Yes you should correct it, from 14th January there will be a correction window available to make changes in the form and the window will be available till 31st january as per my knowledge. So whatever changes you want to do, do them before the time expires. Hope this answers your question.
But they haven't sent any mail toe regarding corrections in photograph or signature. But when I browsed through the correction window only changes in personal details was applicable but not the signature
Yeah! You can log in multiple times to edit details in NEET 2019, but it should before the deadline of application form. Once application from date over you should not be able to edit you details.