Chrome 64.0.3282.140 Stable
Chrome 66.0.3344.0 Canary
Firefox 52 ESR
JAWS 2018
JAWS 18
1.
I can repro this in Chrome stable and Canary, but not Firefox:
# With JAWS running, visit walmart.com
# Turn auto forms mode off JAWS (insert+j) > Utilities > Settings manager > forms mode
I. Issue not present
# Arrow down past the search button
# Pause and wait five seconds

Expected: Works as expected. Navigation of the page is normal

II. Issue presents
# Navigate to edit box
# Press enter to activate forms mode
# Wait five seconds
# Notice that search box is announced again every few seconds
# Press escape to deactivate forms mode
# Arrow down into page content
# Notice that every few seconds virtual focus is returned to the search box

Expected: Focus should not return to the search box

Actual: Focus returns to search and page navigation is not possible

III: Issue initially present, but resolves itself
# Navigate to edit box
# Press enter to activate forms mode
# Wait five seconds
# Notice that search box is announced again every few seconds
# Pres tab
# Notice that now 'search button' is announced every few seconds
# Same is true for 'Reorder items' and 'your account'
# Tab past 'your account'
# Issue is resolved
# Return to edit box
# Notice that 'search' is not announced every few seconds anymore
# Turn forms mode off
# Navigate the page with arrows
# Notice that now navigation works as expected

Note: This solution also works by shift+tabbing in forms mode from the edit box to the home page link. The issue will not re-appear until the page is refreshed and search box focused.

2, 3.
I was unable to reproduce these issues. Works as expected

4.
I was able to reproduce on Firefox and Chrome so assuming this is an issue with website.