Can all NMR spectrometers perform special techniques such as COSY, NOESY, HETCOR,..?
It depends on a lot of things, software-wise


some of these techniques are simply a software option
you can implement pulse sequences yourself, if that´s possible with your control software
you need to have the right software to transform and evaluate the data
... or write it yourself (not exactly rocket science if you know your way with Matlab/Octave etc.)


and also regarding your hardware


you can have several probes for one spectrometer


they can be single channel, or dual ("HX" usually), triple ... channel
the "X" channel can be tuneable over a wide(r) range, or you are limited to e.g. carbon

of course you need a transceiver with enough channels, which can be used at the wanted frequencies
and a suitable preamp for every channel
some techniques need more special hardware, like CPMAS, pulsed gradients, cryo etc.
low field spectrometers on the market (afaik) have no user exchangable parts, so you are stuck with the hardware you bought


But to answer your immediate question: I guess with basically any living (as in "not undead") spectrometer, all those you named above should be possible, provided you can tune the X channel to the het nucleus you are after. They are the basic standards. 

If you want to know a lot more, 200 and More NMR Experiments by Berger and Braun is probably your book.