First, it looks like the bit maybe hasn't been removed in forever, so it could be rusted. A bit of penetrating oil and some time might help.
Second, to loosen the collet, you'd use one wrench to immobilize the router shaft and the second wrench to turn the collet counterclockwise *when viewed straight on from the bit*, not when viewed from the motor.
If/when it breaks loose, watch your fingers. When you reinstall it, it doesn't have to be super tight. In my experience, most people overtighten the collet when they install a bit. Related note, don't 'bottom' the bit when you're installing it. You can push it all the way into the collet, but pull it back out about 1/8" before you tighten it.
Looks OK for the money for small jobs. Be sure it is locked in place so it does not move on you. I rarely used a router not in the table as you get much more control compared to hand held.
If you find you use it a lot you will eventually get a dedicated larger table with a lift.
Small pieces can get away from you and are usually best handled on a table-mounted router. Be sure to always (99%) route _against_ the rotation of the bit. Routing _with_ the rotation can cause the router to get out of control except in very specific circumstances. The last thing you need is for the spinning bit to grab your work piece and throw it across the room. Not because the work piece might embed itself in your garage wall, but because that work piece is likely the only thing between the spinning bit and your fingers.
If your router looks like this one,
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that table isn't likely to be able to accept it. It looks like your router is in the smaller "trim router" category, rather than full size. I don't know of any router tables that accept a trim router, but maybe you can do something custom.
You'll need a router to go along with your new table since your Rockwell won't fit. I like my Bosch EVS1617 2.25HP but every serious tool brand makes a router that will work.
I mounted a router on a wing of my table saw. That way you save space and the same fence or most of the jigs you use for the saw, work for the router too. It did require a little work on the wing but it was worth it.
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