- Do I say I'm a resident of the US for the purposes of applying? Do I need to explain this in my covering letter?
Since your visa has expired and you don't currently have the right to reside in th UK, I'd say you are a resident of the US... you can mention it in a covering letter if you like.
- I have a lost passport, which has a previous Tier 4 visa in it. Do I put estimated dates for both of these and explain in the covering letter?
Yes, I would do that - you have to give details of previous passports and previous visas in the application anyway.
- I can't find the issuing authority on my 2 most recent visas for the UK (Tier 4 and Tier 2). For Tier 2 I put UKVI Home Office as that's who sent me the letter, what should I do about the Tier 4?
What do you mean by 'issuing authority'? What's the exact question on the form?
I'm wondering if they are asking for the consulate which processed the visas (New York) or just UKVI.
- Inputting my previous 5 "visits" to the UK, I've put as the purpose "Former resident", is this correct? My previous 5 "visits" only take me back to 3 Jan '16, is that okay?
Don't you have to cover 10 years of visits to the UK in the visa application?
Just list each entry and exit from the UK over the period (estimating if you don't know exact dates) and write why you were there.
For example, things like
August 2012 - 2 week visit
Sept 2014 - Aug 2015 - Tier 4 visa
- I departed of my on volition on 12 Jan before expiration on 15 Jan, but I don't have any immigration docs for it, do I still say Yes to "voluntarily elected to depart"?
No. You answer NO to that question as it does not apply to you.
It is asking if you have ever been arrested for being an illegal immigrant in the UK and instead of being officially deported, you elected to leave voluntarily before they forcibly removed you.
More questions to come, I'm 100% sure of that. Maybe I need a lawyer. Now I have to remember everywhere I've been! Yikes..
You don't need a lawyer... unless you have serious criminal convictions or you have been in breach of the UK immigration rules in the past.
Just give estimated dates for your travel history if you can't remember.