Do these guys know what they are doing?
Can I safely rely on them to fix this?
They are responsible for rectifying the faults on your roof and should be given the chance to do so.
if you are not fully satisfied with the results employ another contractor and submit the invoice to them.
TBH the job does not look bad! an overweight roofer or seagull with tackety boots has been crunching their way over your roof cracking the tiles.
Dont know whats going on with the membrane! nail holes probably.