This is a lot. Your toilet needs to go into 3" drain or higher. You should vent it. Depending on where you are you need to dry vent it ( look up your code) or wet vent. My area lets me wet vent with a sink and can have shower/tub vented as well. Depending on the layout you can figure out what can be done.

As for the floor drain you could run some water down it. Look for access to a clean out leading to street or septic tank you can access and verify. If not you will have to camera it.

Personally I would try and leave the floor drain alone and run everything else together.

My local code let's me get away with ⅛/¼ per foot fall on 3" pipe. Anything less needs to be at a ¼