What problems is Poland's Law and Justice (PiS) likely to face, given the lack of majority in the Senate?

Question

According to the official results of the Polish parliamentary election, the Law and Justice party (PiS) has won majority in the Sejm (the lower house), but lacks majority in the Senate (the upper house): it has 49 out of 100 senators (including one PiS-aligned independent senator). Such a situation is unprecedented in the history of Polish democracy.

An opinion of the Senate can be rejected by the Sejm:

an opinion of the Senate on an act passed by the Sejm may by rejected by an absolute majority of votes cast by at least half of the statutory number of deputies

Does the Senate have any prerogatives that can make PiS unable to form a functioning government without a coalition? If not, does it have any prerogatives that can stop PiS's controversial Orbán-style reforms? Is it likely that PiS manages to buy two opposition senators' votes in exchange for some favours?

Answer 1

Does the Senate have any prerogatives that can make PiS unable to form a functioning government without a coalition?

No, from politico.eu:

The senate is less powerful than the Sejm. It can delay and amend legislation, but the Sejm can override such moves with an absolute majority.

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If not, does it have any prerogatives that can stop PiS's controversial Orbán-style reforms?

It can block appointments, again from politico.eu:

However, the senate also has a say in nominating many key officials, which will undermine PiS's attempts to put all government institutions under its control.

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Is it likely that PiS manages to buy two opposition senators' votes in exchange for some favours?

It's possible, but the opposition seems to have worked together to try to win the senate. That's a sign that many are committed and believe their partners are committed to putting a brake on the single party in power.

From the Wall Street Journal:

But the opposition benefited from the first-past-the-post system that Poland uses to fill its Senate, and several parties signed pacts unifying behind individual candidates. Under the plurality-based system, the winning candidate is the one who gets the most votes, even if they don’t add up a majority.