Can I somehow make this AV Receiver work properly?

no . A Phono input is a RIAA equalized special input for turntables or MM cartridges, and has no other purpose. All other peripheral devices with standard analog sound output, such as a tape player, use standard Preamp inputs (AUX /TAPE/ AUX2/LOOP/TUNER) If you need more inputs get a switchbox with enough plugs on it to do for you.

Pre-amplified (low-level) signals have an approximate maximum voltage of 1V, like the ones coming out of a CD player, DVD player, Cassette tape player, MP3 player, and all of those labeled "Aux Out", "Direct Out", Rec Out", Tape Out", "Mon Out", "Rec Out", "Loop Out", all of them are similar-level signals.

They can be hooked up to any of the inputs on the "Audio" section on the back of your receiver.

This is also applicable for the front "In" connectors.

To prevent problems, perform every connection with volumes all the way down, or receiver shutdown. Identify all your cables with labels or colored adhesive tapes, post-its, etc.

Now, outputs from a turntable (Phono Outs) are a completely different thing. These outs need to be pre-amplified AND equalized with a special (RIAA) equalization, this is performed ONLY through a "Phono" input.

All of the analog audio connections on a receiver such as the Yamaha 363 can have any device connected to them that has the same kind of connection at the other end.

Looking at the back panel of the 363, you can use either the DVR or MD/CD-R quartet of in and outputs to run a tape deck. For a turntable, in order to connect one to this receiver, you need either an outboard step up preamp, or a turntable that has such a device built into it, as the 363 has no dedicated turntable input. Such turntable inputs on older receivers has a stepup preamp built in, but the relative rarity of turntable without such stepup preamps built in has resulted in most receivers not including the dedicated turntable input.

For play only devices, just use any pair of RCA inputs, such as the DVD or CD inputs The labels on each is merely a convenience for your own use, they are identical aside from the label.

The point of such input labels is to help the user, so if you plug a CD player into the CD input, when you select that input on the receiver, you'll get what the label says. That's easier than having to remember or write down that you plugged the CD player into Input 1, and the tape deck into Input 2.

Your avr does not know what it is connected to, it is just a label on the system. You are fine with everything you have and how you want to connect it.

The only thing you would not want to do is if you have a system with a phono input then you don't stick anything into that except your turntable with no preamp.