6-8 weeks is a good rule of thumb timescale for most people recovering from a resection, but it can vary. Some people will recover faster, especially if they have had a laparascopic procedure.
I agree with this. You may be discharged from hospital after just a few days if all goes well, depending on your surgeon's assessment. The next six weeks or so, you should see a steady improvement in your pain levels, energy and bowel function. Though if there are complications, they are usually minor, but they delay healing a little. E.g. after my last surgery I got an infection, but my GP treated it with antibiotics, so there was no need for me to go back to hospital. You'll need to avoid strenuous activity, bending and lifting for this time because those movements are hard on your abdomen, so you may need someone to help a bit when you first get home (though I know some people manage without, but it's less risky if you keep lifting to a minimum).
I gather from your post that you've been in hospital before for things other than surgery, so I guess you're familiar with what hospital wards are like and what you need to pack, etc. but if you've still questions about it there are plenty of people here who can answer.
Is it the drain in particular that's stopping you wanting to go out? I don't really know what's best, as people feel differently about things like this, but I think I would try just telling people you have it. That's what I do with my stoma. I never feel there's any need to keep it secret. If you tell people straight off that you have the drainage bag, you won't spend the whole time worrying that people will notice.