Will I be able to adjust my status? Since my last entry into the USA was legal

Please talk to a qualified immigration attorney. You will have challenges adjusting, Take your entire FOIA file to the appointment.

APPLICATION FOR PERMANENT GREEN CARD AND PROOFS TO GET IT

You would need an explanation for this 2014 filing and this could be an issue. I suggest you set up a consult with a qualified immigration attorney.

Does immigration do house visits for individuals going through the AOS/green card process?

Yes they can and do , especially in marriage based adjustment cases.

Passive investment is allowed but I would set up a private consultation with a qualified immigration attorney before moving ahead.

Timing the naturalization application with court summons

I would suggest having the ticket resolved, moving and then filing.

If a person previously received H1-B and it expired, does she have to participate in the H1-B lottery again for a new H1-B?

You appear to be cap exempt for another year. good luck

How long does the USCIS take to make this correction and issue a new I-797.

please talk to your attorney, that is why they were hired

I am sorry to hear about your situtaiton. Yes you may be eligible to secure a U visa. U visa could allow you to adjust status and secure LPR status...

I am planning to change my job in 2 weeks to another employer. Does that affect my spouse's EAD application?

If you lose your h1b status then the beneficiary h4 status also does not have the benefit.

H1B to L1B Visa

It depends on the work you are doing.