Another answer is good, but a bit too narrow. So let's talk about it one by one:
Will not burn. There is oxygen in it, but no fuel
One might be concerned about afterburner-like effect. That's not a problem. It's a benefit, if anything. Afterburners work because not all oxygen is used up by main engine. Fuel is used up completely - because carrying fuel is expensive and oxygen is simply there. Thus, engines are designed to avoid fuel waste, not oxygen waste, On a spaceship you may be sure atmospheric oxygen would be taken into account. You will get normal engine exhaust, with less massive rocket (because you don't need to carry oxygen). If your rocket scientist can send rockets to orbit, they will be able to calculate that, no problem.
Oxygen for breathing is already there, isn't it? So nitrogen tanks and mixers will suffice - for about 21% to 25% lower mass. OR lowered pressure somehow. Was good enough for astronauts of Apollo program.
For details, see this answer on Space Exploration.
Interior & clothing
Apollo 1 fire was a big tragedy. But it set a foundation. Nothing in space craft interior will spark again. Nothing in space will be flammable in pure oxygen. Not again. OK, maybe something will, but it really shouldn't. NASA did a huge job to make sure it won't happen, and rules against fire are set high, meant to be suitable to pure oxygen. Other space agencies plan for that as well - better safe than baked. Of course pure oxygen atmosphere is not used anymore, but precautions are set in place.
Rocket engines work with pure liquid oxygen and other strong oxidizing agents. So conditions would be pretty much normal for them. Of course jet engines do not, and that's what you want to use with free oxygen readily available, but materials and knowledge are there. No problem. Just some testing and engineering to match two already related technologies.
This would be a main issue. Stainless steel is brittle. Painted steel is not safe, there is to much risk of scratching it on a planet. Ceramic tiles can be knocked out. For interior it was figured out - but in conditions with moderate temperatures and low risk of scratches.
Composite materials for lander would probably work. Few layers with different properties. And very limited time dirtside. I'm pretty sure it can be done with modern tech. I'd go for steel or aluminium covered with fiberglass covered with ceramics for parts under heavy load, and fiberglass + ceramics for the rest, but I'm no space engineer. Just give them two years, funds and reason and they will make it, sure bet.