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Pokémon training in Sehto is… atypical, compared to the games. Most people keep pokémon as pets and as aids for work they themselves cannot do. Battling is frowned upon, but tolerated - it's hard to completely ignore the Kanto and Johto cultures, after all, even with plenty physical distance to go with it.
Another very important aspect to pokémon - and a reason why many, many people have them - is that they're a cross between 'protectors' and 'weapons', seen as vital for self-defence (especially from other people that have pokémon ^_~). About 25% of all people in Sehto have at least one pokémon (which then in turn usually provides protection for more than one person). Of those, two thirds have at least two.
Having more than five pokémon is considered unusual. Having more than ten is terribly suspicious unless you're a farmer or a pokémon breeder.
PokéCenters
PokéCenters in Sehto are not commonly free. A notable exception is the Togi PokéCenter, which is de-facto communally run (strangers are of course welcome to leave tips); and pokétrainers on the gym circuit may occasionally be granted 'gym leader discounts' when the gym leader announces them and asks for their pokémon to be healed. (That's intended as a favour to the gym leaders, however - very much not the pokémon trainers.)
Prices vary depending on staffing and frequency of their use - understaffed PokéCenters tend to be a little more expensive in an effort to keep their workload manageable and the queues shorter (most notably in Nightclaw) - but shouldn't eat into anyone's reserves too much. Because of the technology used to heal pokémon, prices tend to be batch-prices - the amount of pokémon to heal are divided into batches of six and you pay per batch. As such, getting one pokémon healed costs the same as getting six of them healed.