4 answers
No. You cannot modify the Lead Conversion page layout instead you can create a new custom page and call it from a new custom button.
To your second question, You need to have support to enable the "Apex Lead Convert" feature. Once this was enabled, navigate to Lead Settings and check "Require validation for converted leads". This finally gave me the screen that provided options as to/to not create contacts & accounts.
https://help.salesforce.com/articleView?amp;language=en_US&id=000334707&type=1&mode=1