После ссоры лучше помириться сразу.

After words like лучше, Russian often uses the infinitive to express advice or recommendation:

• лучше подождать = it’s better to wait
• лучше уйти = it’s better to leave
• лучше помириться = it’s better to make up

So помириться is in the infinitive because it names the action being recommended.

This is about aspect.

• помириться is perfective: it means to become reconciled / to make up, with focus on the result.
• мириться is imperfective: it usually refers to the process, repeated action, or general state.

After an argument, the natural idea is reaching the result of reconciliation, so помириться fits better.

Here -ся makes the verb reflexive, and in this case it gives a reciprocal meaning: the people involved make up with each other.

Compare:

• помирить = to reconcile someone
• помириться = to reconcile oneself / to make up with someone

So помириться is the form you use when the people who argued are the ones who later become friendly again.

Russian often leaves that understood from context. This is a general statement, so it means that the people who had the argument should reconcile. If you wanted to name the other person, you would use с:

• помириться с другом = to make up with a friend
• помириться с ней = to make up with her

No, Russian word order is fairly flexible. This sentence is natural as written, but you can also say:

• После ссоры лучше сразу помириться
• Лучше после ссоры помириться сразу

These versions are very similar in meaning. The main difference is emphasis. The original sentence is a normal, neutral way to say it.

More or less:

• После = after
• ссоры = of a quarrel / argument
• лучше = better
• помириться = to make up / reconcile
• сразу = immediately

A very literal version would be After a quarrel, better to make up immediately. In natural English, you would usually say After an argument, it’s better to make up right away.