1.How to Convert '2022-05-01T23:00:00+05:30' this IST time into my local time ? 2. Need to Convert my local time into IST time..

Please check below link 

https://salesforce.stackexchange.com/questions/293375/how-to-convert-utc-to-ist-conversion-in-apex

//Get current date time in GMT format
Datetime dt = System.now();
//Convert it into Indian Standard Time(dtIST).
String dtIST = dt.format('yyyy-MM-dd HH:mm:ss', 'IST');
System.debug('dt-' + dt);
System.debug('dtIST-' + dtIST);