During change of status from F2 to H1B, am I required to be present in USA? Can I go back to my home country meanwhile?

Note that the H-1B petition will be your employer's and not yours. Assuming it will even make it through the most likely inevitable H-1B "lottery" and be ultimately approved , yes, you can depart the US during the time it is pending and then return to the US in July. That will not affect the ultimate outcome of that petition, with the only difference being that perhaps you will not be able "change status" to H-1B while in the USA, but instead will have to briefly depart and consular process for the H-1B visa at a US consulate abroad. But the employer's H-1B petition will not be affected the least bit, for it will be strictly adjudicated on its merits.

Extremely bad plan which may subject you to permanent bars. Work with an immigration attorney.

You must discuss travel plans prior to the filing of your case as well as alert the petitioner and attorney if you need to travel once the H-1B petition is filed and pending. Departure from the US while if the H-1B petition filed by your employer is selected for processing will result in the denial of the "change of status" request. If you are planning to travel, please alert your employer and attorney as to whether you have the required documentation to return in F-2 status and if not, whether it make sense to travel or wait for a decision and then schedule an H-1B visa interview abroad once your H-1B petition has been approved. Also discuss the possibility of expediting adjudication of your case by requesting premium processing service from the USCIS.