1. The government of Israel gives money to yeshivos if it is popular enough to attract votes. If they don’t give the yeshiovos money, the parties who want yeshivos won’t support them. As a result of the last election, the parties favoring support of the hareidi yeshiovos did poorly relative to the anti-hareidim, so the government will cut funding.
2. This is how a parliamentary system works. Each faction joins the government, and gets patronage and money for their favorite projects. It is very democratic and good politics, though from an economic efficiency perspective it stinks (in part because it guarantees high taxes).
3. Conscription is a separate issue. The government might end up saying that they will only fund veterans in yeshivos, but not non-veterans, which is their right. However passing a law that makes it illegal for at least some 18 year olds to learn Torah (requiring them to stop learning and join the army) is unacceptable to much of the frum community.