BPSK modulation under bandlimited channel
1. Matlab can't handle symbolic calculations by itself. You need to use a symbolics-capable package, such as Matlab's own symbolic toolbox, Sage, SymPy, Maple, Mathematica, etc.

2. No, it is not correct. The sequence of -1 and 1 is a sequence of symbols, but what is actually transmitted over the channel is an analog signal. Between the symbols and the channel you need a pulse-shaping filter, which determines the transmitted signal's bandwidth and spectral characteristics.

3. The receive process will depend on the channel's frequency response. Say your transmitted signal has bandwidth $B$. If the channel response is (mostly) flat over that bandwidth, then the channel doesn't distort the signal and you can recover the information present in the signal by matched filtering. On the other hand, if the channel's response is not flat, then the signal will be distorted. In this case, you can perform channel equalization followed by matched filtering. A channel equalizer is a filter that is the "inverse" of the channel; the equalizer's output is an undistorted signal.

I've used a few concepts without explaining them, like pulse shaping and matched filtering. There are already many answers in this site regarding those concepts. If you need further help with these, please leave a comment.