Firstly, I've never managed to have a smooth shave with going with the grain, so I generally shave in both directions. Is it ok to do that?
I've never faced any problems, but it does give a good shave.
Also, how many shaves should I use a cartridge for? Is it better to use the safety razor with blades?
1. Yes, as long as it feels okay.
2. Back when I used cartridge, they lasted about 2/3 shaves. After that they become dull due to the soap/cream/whatever residue clogging up the space between the blades.
3. Yeah, I can get 4/5 full shaves with a single wilkinson and there are much longer lasting blades out there ;)