I know it pretty much means pay or get out, but do they count the weekends as part of the 7 days to pay or get out, or not?
Also, if I move, will I still eventually have to pay and how will this affect my credit?
The word "demand" is different from the word "order", which is what a court would say. This appears to be nothing more than a heavy-handed landlord who is giving you the necessary notice that you will be evicted if you don't pay. On the 8th day, if you haven't paid or haven't left, they can THEN file a court action to evict you. In most states you cannot be evicted until you have been given a chance to pay, given notice to leave, given a court hearing, given an order to leave, and given a chance to comply with that order.

In other words, you probably have another 60 days (depending upon how busy the courts are) before you're phyically thrown out, even if you never pay a dime, if you defy a court order to leave.

Yes, if you owe rent, you will eventually have to pay, even if you move out, and some states allow the landlord to keep your security deposit to cover lost rent and then sue you for any additional damages.

You should also start documenting all of your evidence for good reasons you don't have to pay the rent (unhealthy condition, illegal apartment, landlord violates lease by intruding, etc). Some states prohibit eviction within 6 months of filing a health department complaint against the landlord (assuming it's true).
It means they want the apartment back because you didn't pay your rent. You are getting evicted, and have 7 days to get out (yes, that includes the weekend days). Read the language closely - they may not even give you the option to pay to stay anymore. Eviction notices vary by state.

If you pay and can convince the landlord to let you stay, then it won't affect your credit as badly as if you just leave without paying.

If this is a court order, it will show up on the public records section of your credit report, and future landlords won't want to rent to you because they don't want the hassle of having to evict someone.

Your best approach is to find the rent cash TODAY and call up your landlord offering payment in full to see if they will stop this.

Contact the government office in your community that helps people avoid homelessness and see if they will help. Also, if you belong to a church, often they will help one time with rent assistance.

If you know you are leaving, then work on getting your stuff moved to a safe place like a storage locker. When the sherriff arrives, there won't be time to pack. They will put your stuff out on the curb for anyone to take.
1) 7 days means 7 days….including weekends
2) Yes you still have to pay. It will affect your credit if you fail to live up to the terms of the re-payment.