A: Not at present, but there are indications that this could change. Hamas' charter bars negotiating, recognizing or making any compromises with Israel. For the time being, they are sticking to that line, but even their own officials are saying that such a stance is incompatible with being the leading Palestinian party. Hamas understands that they are going to have to change. One Hamas official has already said that, while Hamas is not prepared for direct negotiations, if Israel has "something to offer, 1,000 ways can be found" to negotiate, which likely means negotiating through third parties.
The Secretary-General of the Arab League flatly stated that Hamas "must" negotiate with Israel and abide by the Beirut declarations of 2002. Based on a Saudi peace proposal, the Arab League in 2002 offered full peace and fully normal relations between Israel and each of the member states of the League in exchange for complete withdrawal from the territories occupied since 1967, the establishment of a Palestinian state on those lands in the West Bank and Gaza, with East Jerusalem as its capital and "Achievement of a just solution to the Palestinian refugee problem to be agreed upon in accordance with UN General Assembly Resolution 194." Israel completely ignored this offer. While there are points Israel would not accept whole cloth, there is no discernable reason that this offer could not be the basis for serious, short-term negotiations aimed at a permanent settlement of the conflict.
In any event, this makes it clear that Hamas is going to face intense pressure to recognize and negotiate with Israel from corners that matter to them. Hamas has always been sensitive to Palestinian public opinion, and that opinion still supports finding a way to end the Israeli occupation and reach an agreement with Israel for a secure and more hopeful future. All these factors combine to suggest that Hamas will, if they form a government, take steps to comply with the wishes of the Arab League and most of the Palestinian populace.