Explaining local politics is fun. The very short explanation is that Puerto Rico is socially conservative but fiscally liberal.
Political parties on the Island are divided by what they want Puerto Rico's political status to be, so the main parties are the Statehood Party, the PPD status quo Party(this one got more complicated recently), and the Independence party. This creates a problem because you might be a Democrat that wants Puerto Rico to be a state or a Republican that wants Puerto Rico to be a state but you have to run under the same party. That's what happened in 2016, the Statehood party won but the Governor was a Democrat while our non-voting Representative and the Presidents of the House and Senate were Republican (I don't have a full breakdown of R vs. D as far as legislators go). In 2008, the opposite happened. The Governor was Republican while our non-voting Representative was a Democrat (Pedro Pierluisi, the same guy that now might be governor).
Mood is a very broad question. I think in general there is fatigue over all the problems the scandals have caused. People don't want the crisis to continue. But the intra-party battle between Schatz and Rosello pretty much guarantee more political drama for the time being. There's been noticeable decreases in basic economic activity in the last couple of weeks between all the protests and everything. The big malls have had to close and when they're open you see a lot less people than normal. Cruise ships have cancelled stops in San Juan which means less tourists spending money.
Maybe broadly people are divided into, those that want the Statehood party to just pick a governor and just wait until the next election or people that don't like either of the two options and would prefer some other solution which unfortunately our constitution doesn't allow. Oh and there's fringe right wingers that think this entire thing has been a plot by feminists and communists to stop Puerto Rico from becoming a state all funded by Venezuela and Cuba.
A full explanation of the differences between Rosello, Pierluisi and Schatz would take probably multiple pages since it would go back to the 1990s and I'd probably say something overly partisan. As some of the articles point out Rosello and Pierluisi ran against each other in the 2016 primary, the differences were really over minor local issues. I'd argue Rosello won the primary because of name recognition; his father was governor from 1992 to 2000, he ran for a third term in 2004 but lost by a very narrow margin. Controversially they forced a senator within the Statehood party to resign so he could serve in the Senate for those 4 years. Pierluisi was Rosello Sr.'s secretary of state. Schatz isn't entirely independent of Rosello, Rosello Sr. named him as Secretary General of the Party in 2002. Might help to think of the Rosellos as a political dynasty like the Clintons. In very broad terms Schatz has been leader of a faction within the Statehood party with back and forth with the Rosellos over the last 18 years.
One of the big disagreements right now in the Rosello/Schatz/Pierluisi debacle right now is that Pierluisi worked until Wednesday for a Law Firm that was employed by the Fiscal Oversight Management Board. When the Island defaulted on it's debt, as a territory it lacked bankruptcy protection. Congress created a new law PROMESA which allowed for a bankruptcy process, in exchange for that benefit a Fiscal Board was installed to guarantee the Island would balance the budget. Politicians from the Statehood and PPD parties went to congress to lobby for both bankruptcy protection and a Fiscal Board (Junta in spanish). Once the board members were picked by the Obama admin they became the local villains for politicians on the island. Rosello and legislature have been at war with the board over the last two years. It's clearly had an effect on voters, early on the board had over 60% approval rating, it's dropped below 40% in recent polls. My personal opinion is that this was an intentional political strategy. Puerto Rico was running a budget deficit of about 30% prior to defaulting. The board allows politicians here to outsource cutting the budget to the Fiscal Board so that they get the blame and local politicians don't pay a political price at the polls for cutting services and raising taxes. Unfortunately for Pierluisi, because he worked for the Board, Schatz and critics of the board are using that to argue he's aligned with the Board rather than with local interests.