For those who don't know about ATC radar, I hope the following can help a little.
An example of a relatively modern primary surveillance radar (PSR) produced by SELEX - the ATCR-33S - is quoted as having a detection range of 60-100 NM in S-band. I recall that the lower limit is a guaranteed level of performance in bad weather with some failed transmit modules, so a fully functional radar in good weather is likely to exceed the upper limit quoted.
They have another model that works in L band which is claimed to have a range of approximately double that - so 100-200 NM.
I would imagine that the ranges quoted above would be typical of PSR available in relatively modern ATC systems that wanted primary radar. Legacy systems from the 1970s and 80s would likely be at the lower end of the quoted ranges, but almost anything is possible with enough watts. Military specific radars are likely to have longer ranges.
PSR can give some idea of altitude because (some types) can scan "beams" at different angles to the vertical and have processors that convert the angle plus the range into height, but this isn't going to be precise.
Secondary Surveillance Radar (SSR) generally has a significantly longer range than primary, because it relies on the aircraft transponder replying to an interrogation pulse. The return signal identifies the aircraft and should by now also include height data.
Without confusing matters by attempting to go into the details of Mode-C, Mode-S etc, ADS-B as used by the public air traffic websites relies on an (ad-hoc network of) receiving antennas that eavesdrop on the replies from (extended) SSR interrogations. The receivers decode extended data that is generated by the aircraft, but are susceptible to overlapping transmissions by other aircraft in range, and I suppose by other RF noise.
*IF* ADS-B data is received correctly by a receiving antenna *AND* the aircraft was transmitting its position (and altitude) data correctly *THEN* the position reported should be correct.
If however the data packets were corrupted by other transmissions, or the aircraft was no longer reporting its position correctly, you could receive anything, or nothing. There are mechanisms (checksums, for example) that should reject corrupted data, but nothing is foolproof.
Apologies in advance to those I've offended by errors, omissions or by teaching the art of egg sucking. This was intended to be a simple factual post. As always, corrections are welcome.