Learn Russian: Мы советуем этот режим друзьям, причём он очень полезный. - We recommend this routine to friends, moreover, it is very healthy.

While и just links two facts, причём adds significant, often emphasizing supplementary information. Here, it acts like 'moreover' or 'and what's more,' highlighting that the routine has the added bonus of being very healthy.

Why is друзьям in the dative case?

The verb советовать (to recommend or advise) takes the accusative case for the thing being recommended (этот режим) and the dative case for the recipient of the advice (друзьям).

Doesn't режим usually mean a political regime? How does it mean 'routine' here?

While режим can mean a political regime, in everyday Russian it very commonly refers to a regimen, schedule, or mode of operation (like режим дня for daily routine or a diet/exercise regimen). Given the context of it being полезный (healthy), 'routine' or 'regimen' fits perfectly.

In the second clause, does он refer to the friends?

No, он refers back to режим (routine), which is a masculine singular noun. If it referred to the friends, the pronoun would be the plural они and the adjective would be полезные.