Question about Canon EF 2x III teleconverter

Mechanically, the Telekonverter will fit your 500D, as well the lenses you have listed.

The problem will be the autofocus (AF)! You need to check on the EOS 500D manual what is the maximum aperture value for your AF points. I am pretty confident that you will not have AF. with any of your listed lenses and your EOD 500D body.

Manual focus should not be a problem.

I do own a 2x TC, and if I try to use it on my EF 100-400mm (either on my Canon 7D or 5D), I do not have AF. Same goes when using my Sigma 50-500. No AF, but MF is available. A bit tricky to nail the focus, depending on what you shooting. Highly recommend you to use a reasonable tripod!

Finally, there is a "light problem": if we take your Tamron as an example, with the 2xTC, you minimum aperture will jump from f/5, to f/11! Essentially, you loose 2 stops of light!

Hope it helps!

Marcel

I should remark that I bought the doubler as a way to get to 400 mm without either spending a fortune or having to carry another heavy lens. So far I have been very impressed indeed with the quality of the results when using it with an EF 70-200 F 4.0 L IS USM. Thus, I can recommend the price/performance of the doubler without reservation.
Of course, using a doubler halves the amount of light, so the max aperture of my 70-200 is reduced from F4 to F8. This will surly kill the auto focus as Marcel (above) remarks. The AF at F8 does work perfectly with my EOS-R, but that is a very different question.
Thus:
1. The doubler will work with the 500D I think, but with the problem mentioned concerning AF.
2. & 3. I have an EOS 70D with an EF-S 15-85 F 3.5-5.6 IS USM. However, I do not believe that this will work with the doubler because the rear element of the EF-S lens sticks out too far. This is presumably the same reason that an EF-S lens cannot be fitted to a Full Frame Canon body. Thus, I doubt that either of the EF-S lens mentioned will work with the doubler, although you may be able to check compatibility with Canon. A quick Web search gives the same opinions.
4. If the Tamron is designed for a Full Frame "EF" body, which I think it is, it will probably work. Check that the rear element does not protrude further back than the seating flange. However, halving the aperture of an F5/6.3 lens will leave very little light, especially given the issue of noise with an 11 year old sensor.

Many thanks for the answers to the above compatibility questions. Much appreciated.