Re: partial laminate floor replacement
Some saws use a wing nut, others a knob to release the plate for adjustment, and I would almost bet the farm yours is adjustable. Don't take this personally or anything of the sort, but it sounds like you haven't had much experience using a circular saw, and this type of repair calls for tilting/tipping the blade down onto you desired mark, by holding the front of the bottom plate against the floor, and with the back-end raised...then slowly lowering the spinning blade onto your cut-line. You might wish to have a friend or someone more experienced do the initial cut-out.
You could also attempt removal by making a few pass's with a router or laminate trimmer{again using a straight edge as a guide}. There a few types of hand saws that could work as well, a Japanese pull saw is one I can think of offhand, though very tedious work. Last resort I can offer is, if it's that thin, you could spend the time with a razor knife making a whole bunch of pass's lol.
Maybe others here will join in with other solutions...best of luck!