Are Plastic doors of the Nakamichi RX505 and Nakamichi RX303 the same?

yes

Nop, don't do that, the subwoofer power in the Nakamichi Soundspace 8 is 20 Watts and the subwoofer for Nakamichi Soundspace 9 is 70 Watts. If you put the 20 Watts Subwoofer on a 70 Watts input the subwoofer will receive severe damage. http://www.nakamichi.com/pdf/SS8_brochure.pdf
http://www.nakamichi.com/pdf/SS%209%20Brochure.pdf

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Not sure on the exact model number these sites may have the manual but not sure on model number so cannot be certain

http://www.hifi-manuals.com/Nakamichi/Soundspace-10-service-manual/download
http://www.nakamichi.user-manuals.com/nakamichi-c-68.html?page=1&sort=2a
http://www.user-manuals.com/user-manual-NAKAMICHI-1000II.html

I'm not familiar with this product, and there the best I offer is that you consult the user guide (which you probably already have)
http://www.ps2netdrivers.net/manual/nakamichi.ta-4/#manual
or (buy) a service manual (which it seems includes a troubleshooting guide) from any of a number places, two are given below:
http://www.manualszone.com/en/nakamichi-service-manuals/62888-NAKAMICHI-TA4-service-manual.html
and
http://www.nakamichi.owner-manuals.com/TA4-service-manual-NAKAMICHI.html
All three manuals/guides are available from
http://www.hifiengine.com/manual_library/nakamichi/ta-4.shtml
There other websites where you an download the service manual (I don't know if the are the 'official' service manual, or different ones that have been written by different people).
If you are really stuck contact Nakamichi through www.nakamichi.com or (what appears to be a more friendly site) http://www.nakamichi.co.uk/support

24.August.2014

The problem is almost certainly that the belt for the CD tray is fatiguing. When this happens it becomes too loose to do its job. The solution is to replace the belt, of course, but it's not a job for the faint of heart. Getting at the belt is fairly involved.

There is a temporary fix, though. If you remove the top cover of the CD player (with the machine unplugged) and look at the right rear corner of the CD tray, all the way to the back of the unit, you will see a little spring-loaded white plastic roller that fits into a notch on the tray. This is to keep the tray from flopping open and from moving in or out during play. The belt will be slipping too much to overcome the grip that the roller has on the tray. You can carefully bend the spring out just enough to allow the belt to do its job but at the same time allowing the roller to still do its job.

This is a temporary fix. Eventually the belt will reach a point where it doesn't have enough grip on the pulleys to open the tray at all. It might even just break and fall off but this fix will allow you to use the player until you're ready to replace the belt.

ebay

The CD player muigt be able to rescue by a reset top factory settings, mostly available in your manual, the cassette deck i think needs to be repaired.

NEW CABLE FROM NAKAMICHI IS £150 . INSTEAD JUST CUT THE METAL SHIELD OFF ANY CD MINI DIN CONTROL CABLE WITH A JUNIOR HACKSAW AND IT WILL FIT PERFECTLY (IT ONLY GOES IN ONE WAY BECAUSE OF THE WAY THE PINS ARE LAID OUT!). I USED AN OLD MAC DIN PLUG BECAUSE IT WAS 3M LONG! WORKS PERFECTLY!

DS

I had sorta the same problem and I just fixed it. Mine was making clicking noises and jerking the tape causing speed variations and pitch changes, Uggghh. The FF, Rew, and take up functions are not belt driven like most decks. There is a little idler wheel between the motor and the take up axle. Take the whole transport assembly loose from the front of the deck...slide it back 3 inches . Take off the ground wire screw, and 3 screws holding the transport mechanism in place :...1 screw on top, 2 on bottom. Take the black front faceplate off of the drive...2 little screws. This exposes everything.The little idler wheel has a press on tiny,tiny piece of clear plastic holding it onto its little axle. Be hella careful. Use a tiny eyeglass screwdriver to pry it up and off. Dont lose it. Pull the idler wheel off. The rubber has hardened and slips. Pry the rubber rim off of the white plastic pulley using the tiny screwdriver. Put on an O ring that just fits. Scruff up the perimeter of the O ring with 220 sandpaper, Easy does it. Idler wheel goes back in, press on the little plastic retainer, put the black metal plate back on( 2 screws at top), slide the transport mechanism back into the front panel, secure with 3 screws, ground strap, replace cover. Clean heads, demagnetise, badda bing, badda boom.