What we would like to change are finishes such as the backsplash and countertops. Is this feasible to do without damaging the cabinets?

Should be - I'm doing this right now in my current remodeling with most of my house cabinets.

Here is a before-and-after example of my master bath (kept cabinets, hardware and lighting, everything else was replaced/renewed - still in progress, e.g. missing mirrors):

Before:

After (in progress):

in what order should these projects happen?

Pros or people with more experience can chime in as well, but I'd say:

1. paint cabinets and crown molding
2. change countertops
3. change backsplash
4. refinish hardwood floors

I'm certain about changing countertop should be before changing backsplash. Refinish hardwood floors should probably be the last thing do be done, to minimize dirt/damage to it post re-finishing. and I would make painting the cabinets first, in order to not splash paint on brand new countertop/backsplash.

Make sure to pick *everything* in advance - to make sure that everything goes with everything else, especially if you plan to perform the project in phases spanning a long period of time. You don't want to paint a cabinet a color that may not work well with a countertop slab that you will fall in love with at a later phase.

Those cabinets are stunning and the layout looks good. They're cherry?

I'd change the backsplash and counters and leave the rest as is. Paint eventually chips. I have factory made cabinets and there are a few small areas after five years that need touchups. In my condo, I had cherry cabinets and the last time I saw them which was when they were 8 years old (we sold the condo but wound up being friends with the new owner), they still looked brand new.

I would probably tile around the whole window.

I am with cpartist. The cabinets are lovely. It would be a shame to paint them. I like the perimeter counters but not the island counter. I like the backsplash too. The floors need some love. Let me guess. You want to paint the cabinets white?

Yes, you can change countertops and backsplash with existing cabinets. We did our second kitchen redo about 5 yrs ago and kept the existing layout and cabinet boxes, but did new overlay soft close doors and drawer fronts and painted white. Paint first, then the counter. If you are using the counter material also as your backsplash, no issue. If you decide to use a different backsplash, I would wait to finalize that choice until AFTER the cabinets are repainted and the counters are in. Then you can hold up backsplash tile samples and be sure about your choice. I do actually like your wood cabinets, though, and I rarely like wood cabinets!

Those wood cabinets look gorgeous -- please don't paint them! (The perimeter cabinets.)

The layout is very good, I can see why you're happy with your Kitchen.

If you're looking for a change, change the counters & blacksplash. Maybe change the knobs/pulls?

It looks like the island is painted, maybe re-paint it for a change as well? (The island cabinets look like they have some chips & scratches, so re-painting them would fix those -- at least for awhile. Painted cabs will generally show more wear & tear over time than stained or natural wood. My old Kitchen had painted cabs and they definitely started to show wear & tear after a few short years. My "new" cabinets are stained wood and after 15 years, people still think they're brand new.)

We did exactly that 2 years ago with virtually the same cherry cabinets.

Before

After