I am wondering, when does the processing time for adjustment of status begin to run?
1. AFAIK the date USCIS receive your valid application - I understand validity includes all required documents and fees submitted so if such is a check that it will be cashed and the funds obtained.
I submited my documents in January. When I still had a valid I-194, but I haven't heard from them, and now my I-194 is expired.
Does it count as I filled within my legal period or afterwards?
2. Filing during the validity of I-94 as you have keeps you in status.
What happens if they return the application and/or request more documents? Will that that count as filling after my I-194 was expired, or will they considered the first date in which I filled and I was legal.
3. See 1 - AFAIK a request for more info is considered as per 1st submission date but if form returned and you submit then the day USCIS receives it is day 1. If the latter is after I-94 expiry then you are out of status. If you are AOS as the spouse of a USC then this 'out of status' position is not a major issue since the Immigration Act paroles (forgives) this overstay but not any subsequent bans were you to depart the US (see below re consular filing).
Would I be deported if an officer asks me for my papers and I don't anything from USCIS demonstrating my petition is in proces?
4. Why would you get deported? Send your paperwork with an option confirming delivery - the US postal service will give you various options or you can use a courier like Fedex. USCIS should also send a receipt for your fees which could be used as evidence they received the application.
If I get deported, could I still try the consular way to come to the US and live with my husband?
5. Why would you get deported? If you are deported consular filing won't work - you need to get a waiver. Consular filing won't work either if you are subject to the overstay bans unless you get a waiver. Waivers are difficult to obtain and require you to demonstrate extreme hardship to the USC due to your refusal to enter the US. Without further info on your US immigration history to include your AOS category (spouse etc) I can't comment conclusively on this.
