You can use all the banes and boons you have access to through your attributes, provided you can explain what exactly your character is doing to invoke them (it would be odd for an illusionist to use their Influence to inflict the Dominated bane, for example). Generally though, most players I’ve come across will use 3-4 banes and 2-3 boons. That’s not a rule, just what I’ve seen and a good range to aim for when writing up favoured actions on a character sheet. It’s helpful to know what else you have access to on top of that (for situationally useful effects like Disarmed or Light) but knowing half a dozen banes and boons for your character at a glance makes combat run more smoothly.
I am very much against your idea of limiting boons based on your level: it only subtracts from the game instead of adding, it makes boon-heavy support builds almost impossible at low levels, and it’s one more thing to keep track of that doesn’t need tracking. What I’d suggest instead is that you have your players write down a short list of the boons they think they’ll do most often and give them a flavourful name to explain what they actually do (like a Heal boon through the Presence attribute might be an “encouraging shout”) for quick reference and if a situation comes up where they might need something that’s not on the list they can look it up and come up with an explanation when it happens. If some of your players want to keep to the level restriction then they’re welcome to, but you should make it clear that the rules of the game don’t enforce it.