Is DCT basicly a filter?
DCT and DFT can be thought of as a bank of bandpass filters.  So it's sort of a filter, but it doesn't remove any part of the signal.  The whole signal is still there, just in a different format.

Yes, you could do the DCT on the signal and then high-pass filter by multiplying by the DCT of a high-pass filter's impulse response.  I'd suggest using DFT/FFT first though; it's a little more intuitive, though for a final application DCT has better energy-compaction, and so can compress signals better.