If i apply for h1b from h4 visa then can i leave usa for that visa conversion time?

You may only change status while in the United States. You may obtain a H for hat the US consulate while out of United States.

Can i apply for citizenship although i lost my green card,but i apply for green card replacment

You may apply for naturalization without resident card

What is the time needed to get c.p.t of F1 visa from H4 visa?

There is OPT - Optional practical training and CPT curricular practical training OPT may take 90 days. CPT see your DSO

It may affect the timing and it may raise questions about becoming a public charge.

Do Infopass appointment makes my difference for file been sitting for a while..

In some cases yes, in some other cases no. 5 weeks is not long with CIS

I apply for green card replacement how long it takes to receive it?

Normally about six months. Check processing times at www.uscis.gov

Nautralization - Passed the interview and officer informed me she will send case for supervisors review

Different officers and matters take different lengths of time be patient wait a month or so. No need to apply for renewal of resident card at this...

Drop-Box for H4

If your prior visa as an H-1 with the same petitioner is still valid. Since you changed employers/petitioners the visa appears to be no longer with...

Anything can be done with a closed case?

If possible you may want to begin again. Regardless, you should discuss with your employer's attorney or obtain counsel on your own to review your...

J1 and J2 filing together with EAD

This is permissible go ahead and file.