The only compatibility problem you'll have is that none of the software you've bought for your Windows machine will work with a Mac. But yes, there's a version of Office for Mac and no, it doesn't matter who your broadband provider is. I don't know for sure but if you use a USB broadband modem you might have issues with drivers but you'll have to do the research on it.
Macs are a delight to use; but before you bin your existing machine, why don't you try and solve the problems it seems to have? Do you run Windows Update regularly, do you use antivirus that you keep updated and scan the machine with regularly, do you run realtime anti-malware, do you scan regularly with up-to-date definitions for trojans, spyware and adaware? It's not a huge amount of effort but it does need to be done with a Windows computer and if you don't, you have only yourself to blame.
Or is it a hardware problem? If so, have you been back (and back and back) to the shop that sold you the machine? It's a shame to junk a computer if you can sort it out.