Learn French: Cela m'arrange de partir plus tôt.

In this sentence, the verb is actually the non-pronominal arranger, and m' is just a direct object pronoun meaning 'me'. While the pronominal s'arranger means 'to work out' or 'to be fixed' (as in ça va s'arranger), the idiom arranger quelqu'un means 'to suit someone' or 'to be convenient for someone'.

Why do we need the word de before partir?

When you use a dummy subject like cela or ça at the beginning of a sentence, French often requires de to introduce the real action that follows. If you put the action first, the de disappears: Partir plus tôt m'arrange.

I always confuse plus tôt and plutôt. How can I tell them apart here?

Plus tôt as two words literally translates to 'more early' (earlier), which fits perfectly with leaving. Plutôt as a single word means 'rather' or 'quite'. A good trick is to see if you can replace it with plus tard (later) — if you can, you need the two-word version!

Can I say ça m'arrange instead of cela m'arrange?

Yes, you will hear ça m'arrange all the time in everyday spoken French! Cela is just a slightly more formal version of ça, but they are completely interchangeable here.