diff --git a/apps/trading-e2e/src/integration/closed-markets.cy.ts b/apps/trading-e2e/src/integration/closed-markets.cy.ts
index 08c1819ba..2778d1845 100644
--- a/apps/trading-e2e/src/integration/closed-markets.cy.ts
+++ b/apps/trading-e2e/src/integration/closed-markets.cy.ts
@@ -450,3 +450,17 @@ describe('Closed markets', { tags: '@smoke' }, () => {
       .should('have.text', 'View on Explorer');
   });
 });
+
+describe('no closed markets', { tags: '@smoke', testIsolation: true }, () => {
+  before(() => {
+    cy.mockTradingPage();
+    cy.mockSubscription();
+    cy.visit('/#/markets/all');
+    cy.get('[data-testid="Closed markets"]').click();
+  });
+
+  it('can see no markets message', () => {
+    // 6001-MARK-034
+    cy.getByTestId('tab-closed-markets').should('contain.text', 'No markets');
+  });
+});
diff --git a/apps/trading-e2e/src/integration/market-all.cy.ts b/apps/trading-e2e/src/integration/market-all.cy.ts
index f576a6ee5..9aee10bce 100644
--- a/apps/trading-e2e/src/integration/market-all.cy.ts
+++ b/apps/trading-e2e/src/integration/market-all.cy.ts
@@ -1,7 +1,10 @@
+import { aliasGQLQuery } from '@vegaprotocol/cypress';
+import type { MarketsQuery } from '@vegaprotocol/markets';
 import * as Schema from '@vegaprotocol/types';
 
 const rowSelector =
   '[data-testid="tab-all-markets"] .ag-center-cols-container .ag-row';
+const colInstrumentCode = '[col-id="tradableInstrument.instrument.code"]';
 
 describe('markets all table', { tags: '@smoke' }, () => {
   beforeEach(() => {
@@ -60,7 +63,7 @@ describe('markets all table', { tags: '@smoke' }, () => {
     // 6001-MARK-035
     cy.get(rowSelector)
       .first()
-      .find('[col-id="tradableInstrument.instrument.code"]')
+      .find(colInstrumentCode)
       .should('have.text', 'SOLUSD');
 
     //  6001-MARK-036
@@ -155,6 +158,7 @@ describe('markets all table', { tags: '@smoke' }, () => {
   });
 
   it('able to open and sort full market list - market page', () => {
+    // 6001-MARK-064
     const ExpectedSortedMarkets = [
       'AAPL.MF21',
       'BTCUSD.MF21',
@@ -167,8 +171,38 @@ describe('markets all table', { tags: '@smoke' }, () => {
     cy.get('.ag-header-cell-label').contains('Market').click(); // sort by market name
     for (let i = 0; i < ExpectedSortedMarkets.length; i++) {
       cy.get(`[row-index=${i}]`)
-        .find('[col-id="tradableInstrument.instrument.code"]')
+        .find(colInstrumentCode)
         .should('have.text', ExpectedSortedMarkets[i]);
     }
   });
+
+  it('can drag and drop columns', () => {
+    // 6001-MARK-065
+    cy.get('.ag-overlay-loading-wrapper').should('not.be.visible');
+    cy.get(colInstrumentCode)
+      .realMouseDown()
+      .realMouseMove(700, 15)
+      .realMouseUp();
+    cy.get(colInstrumentCode).should(($element) => {
+      const attributeValue = $element.attr('aria-colindex');
+      expect(attributeValue).not.to.equal('1');
+    });
+  });
+});
+
+describe('no all markets', { tags: '@smoke', testIsolation: true }, () => {
+  before(() => {
+    cy.mockTradingPage();
+    const markets: MarketsQuery = {};
+    cy.mockGQL((req) => {
+      aliasGQLQuery(req, 'Markets', markets);
+    });
+    cy.mockSubscription();
+    cy.visit('/#/markets/all');
+  });
+
+  it('can see no markets message', () => {
+    // 6001-MARK-048
+    cy.getByTestId('tab-all-markets').should('contain.text', 'No markets');
+  });
 });
diff --git a/apps/trading-e2e/src/integration/market-selector.cy.ts b/apps/trading-e2e/src/integration/market-selector.cy.ts
index 8a5fa15f3..42792e2b3 100644
--- a/apps/trading-e2e/src/integration/market-selector.cy.ts
+++ b/apps/trading-e2e/src/integration/market-selector.cy.ts
@@ -25,6 +25,7 @@ describe('markets selector', { tags: '@smoke' }, () => {
     cy.wait('@MarketsCandles');
   });
 
+  // 6001-MARK-066
   it('can toggle the sidebar', () => {
     cy.getByTestId('market-selector').should('be.visible');
     cy.getByTestId('sidebar-toggle').click();
@@ -84,7 +85,7 @@ describe('markets selector', { tags: '@smoke' }, () => {
       });
   });
 
-  // 6001-MARK-27
+  // 6001-MARK-027
   it('can use the filter options', () => {
     // product type
     cy.getByTestId('product-Spot').click();
@@ -94,7 +95,7 @@ describe('markets selector', { tags: '@smoke' }, () => {
     cy.getByTestId('product-Future').click();
     cy.getByTestId(list).find('a').should('have.length', 4);
 
-    // 6001-MARK-29
+    // 6001-MARK-029
     cy.getByTestId(searchInput).clear().type('btc');
     cy.getByTestId(list).find('a').should('have.length', 2);
     cy.getByTestId(list).find('a').eq(1).contains('BTCUSD.MF21');
diff --git a/apps/trading-e2e/src/integration/markets-proposed.cy.ts b/apps/trading-e2e/src/integration/markets-proposed.cy.ts
index de9c5a13d..1cb30314c 100644
--- a/apps/trading-e2e/src/integration/markets-proposed.cy.ts
+++ b/apps/trading-e2e/src/integration/markets-proposed.cy.ts
@@ -1,16 +1,16 @@
-import { checkSorting } from '@vegaprotocol/cypress';
+import { aliasGQLQuery, checkSorting } from '@vegaprotocol/cypress';
+import type { ProposalsListQuery } from '@vegaprotocol/proposals';
 
 const rowSelector =
   '[data-testid="tab-proposed-markets"] .ag-center-cols-container .ag-row';
+const colMarketId = '[col-id="market"]';
 
 describe('markets proposed table', { tags: '@smoke' }, () => {
-  beforeEach(() => {
-    cy.clearLocalStorage().then(() => {
-      cy.mockTradingPage();
-      cy.mockSubscription();
-      cy.visit('/#/markets/all');
-      cy.get('[data-testid="Proposed markets"]').click();
-    });
+  before(() => {
+    cy.mockTradingPage();
+    cy.mockSubscription();
+    cy.visit('/#/markets/all');
+    cy.get('[data-testid="Proposed markets"]').click();
   });
 
   it('can see table headers', () => {
@@ -35,10 +35,7 @@ describe('markets proposed table', { tags: '@smoke' }, () => {
 
   it('renders markets correctly', () => {
     // 6001-MARK-049
-    cy.get(rowSelector)
-      .first()
-      .find('[col-id="market"]')
-      .should('have.text', 'ETHUSD');
+    cy.get(rowSelector).first().find(colMarketId).should('have.text', 'ETHUSD');
 
     //  6001-MARK-050
     cy.get(rowSelector)
@@ -119,6 +116,7 @@ describe('markets proposed table', { tags: '@smoke' }, () => {
       );
   });
   it('proposed markets tab should be sorted properly', () => {
+    // 6001-MARK-062
     cy.get('[data-testid="Proposed markets"]').click({ force: true });
     const marketColDefault = [
       'ETHUSD',
@@ -196,4 +194,31 @@ describe('markets proposed table', { tags: '@smoke' }, () => {
     ];
     checkSorting('state', stateColDefault, stateColAsc, stateColDesc);
   });
+
+  it('can drag and drop columns', () => {
+    // 6001-MARK-063
+    cy.get(colMarketId).realMouseDown().realMouseMove(700, 15).realMouseUp();
+    cy.get(colMarketId).should(($element) => {
+      const attributeValue = $element.attr('aria-colindex');
+      expect(attributeValue).not.to.equal('1');
+    });
+  });
+});
+
+describe('no markets proposed', { tags: '@smoke', testIsolation: true }, () => {
+  before(() => {
+    cy.mockTradingPage();
+    const proposal: ProposalsListQuery = {};
+    cy.mockGQL((req) => {
+      aliasGQLQuery(req, 'ProposalsList', proposal);
+    });
+    cy.mockSubscription();
+    cy.visit('/#/markets/all');
+    cy.get('[data-testid="Proposed markets"]').click();
+  });
+
+  it('can see no markets message', () => {
+    // 6001-MARK-061
+    cy.getByTestId('tab-proposed-markets').should('contain.text', 'No markets');
+  });
 });