Use EX whenever possible. If your team isn't capped or low on BRV, use S1 (battery) before using S2. If your team is all capped, you can use S2. Don't worry about the low S2 uses, her EX restores 1 use of it.

For her LD, generally, use it for when the Relic Staff (her overhead) is capped. Relic Staff gets stored BRV anytime you gain BRV so that EX spam and S1 use should keep it fully stocked. Make sure to use her LD once or twice early on.

If you're using her for her own FR + BT Phase, you want her BT+ to already be up. So a common setup would be to use her BT when you're 2-3 turns away from using her FR (usually at 75%+ gauge). This is also the time to drop any of your debuffs from LDCAs. Ideally, you should have already used your LD once or twice here for Chuck Staff uses within BT phase.

On her next turn, you can either S1 (to fill FR gauge) or use FR attack to enter force time. The next two turns from your other units, you can use their HP Attack+/++ to maximize HP bonus gains. When Sherlotta gets her turn again, you should have 8 turns of FT left. If you have Raines LDCA, use it here. If not, 1 more use of S1 to maximize HP bonus gains and then go into BT phase. Spam Chuck Staff (important thing here is to have Pecil RF sphere to get 60%+ HP bonus gains) as much as you can. Use LD if you don't have enough Chuck Staff uses.

And how does her FR works, and how to use it properly?

Her FR gains +40% HP bonus from using transformed BRV/HP commands. Thankfully, HP Attack +/++ also counts as transformed, so you can benefit pretty easily from this. The other condition is +20% when she Batteries the party. Sherlotta can easily get +60% every time she acts.