yes its safe to use in that way, i heard sometimes people use broken or cracked screen mobile for long duration such as 1 year

you should reset your mobile, if its doesn't solve then do By DIY online flashing ( not recommended ) or visit nearby software repairing shop, or you can also visit LG care.

laser machine is required to fix this kind of work you can watch the ifixit article here , usually at local market ``iphone x back glass replacement`` will cost you 40$

may be battery got drain so thats why your mobile is not showing any sign, in this case plugin charger for while ( 1 hour) even its not showing any sign, second thing is as you said week ago you replaced battery it may be battery fault, contact the dealer or seller you bought from. above information provided by ``krishna online store``

it will cost you in indian currency nearby 7500/- this service is only available in major cities, if you go to authorised center then they will suggest to replace whole folder ( screen and touch ) source : krishna online store pune