Yes to both, with some caveats. Adding a battery to an existing array is, as owners puts it, no more dramatic than replacing a failed inverter — any competent solar installer should be willing to do it, and the effort is lower than a full install from scratch. The main thing to check is your inverter: if it's a string inverter, you'll likely need to swap it for a hybrid one to take a battery, which is part of the cost. A smaller independent installer is often happy to take this kind of add-on work that bigger outfits skip.
Retrofitting optimisers to existing panels is also doable, especially if the panels are accessible (for example on a flat roof). It's broadly a matter of fitting one per panel that suffers shading, but there are details that matter: record each optimiser's serial number and its position (photograph a layout card) before you fit them, because you'll need those serials if you later add monitoring that has to discover and pair with each unit. It's worth confirming first whether your install already has optimisers — you can check by comparing the volts per panel against an un-optimised string, where optimised panels read a few volts lower each.
For both jobs, remember the VAT angle: a battery added later to an existing system attracts 13.5% VAT, unlike the 0% rate when bought with the original PV install. So weigh the retrofit cost (new hybrid inverter plus battery plus VAT) against what you'd have paid doing it together. If you're fairly sure you'll want storage eventually, going battery-ready at first install is usually cheaper — but retrofitting is entirely possible if you didn't.