I would think "workbench casters" would be a good option to permit the greatest stability when you don't need to roll around often. Mounting them on the legs may be an issue, tho.

https://www.amazon.com/SOLEJAZZ-Workbench-Retractable-Construction-Urethane/dp/B07V6X2LNB/

In my experience, yes. Especially if you’re not on a perfectly level floor. For things I don’t want to move when I’m using them I prefer the casters that set the bench down on the floor when you’re not moving it. Like these:

https://www.amazon.com/dp/B07V6X2LNB/ref=cm_sw_r_cp_api_glt_fabc_CY57FW1HS6NFAP6VH4VK