Q1: After Alignment step, should I call the peaks separate for each
input and experiment replicate and then i should find the common peaks
between all the replicates of input and experiment?
There isn't a standard approach that everyone takes. ENCODE has an IDR (Irreproducible discovery rate) pipeline to get a combined set of peak calls from replicates, but it's mainly for TF ChIP-seq. I've used it for narrow marks like H3K4me3 and it works ok, but I don't think you'll get much from it with a broad mark like H3K27me3. I've seen people just keep peaks with >50% overlap between replicates. I've also just seen people combine their alignments from all replicates into a single bam and do peak calling on that. I think the first method is more stringent, so you'll get less false positives but probably miss some true positives.
Q2: Ultimately i want to find differential peaks between parent vs
resistant cell lines. How can I achieve this? Should I use homer?
You can just look at the peak calls and compare peaks that are called in one group and not called in the other. If you get interesting results from that, then great. Otherwise, there are various tools out there to look at differential levels of enrichment. Macs2 has a diffpeak operation, there's a fairly new tool called NormR that does differential enrichment. I've also seen papers that call peaks, get the read counts within each peak, and then do a standard DEG-like analysis using, for example, EdgeR or DESeq2.