Is placing a tissue at the anal opening after purification due to an anal fissure, in order to maintain purity and prayer, considered a correct action? And is refraining from surgery due to fear and shyness considered a sin? And is the prayer valid while this situation persists?

If the discharge of blood traces is continuous, then your ruling is that of a person with incontinence: you should take precautions by placing a cloth or tissue, and perform ablution (wudu') after the time for prayer has begun, and pray with that ablution whatever obligatory and supererogatory prayers you wish until that prayer time exits.

For the Malikis, there is a facilitation by not obligating ablution (istinja') and ritual purification (wudu') for every prayer for a person with incontinence.

However, if you find a time slot that is sufficient for prayer without anything discharging, then you must pray with a valid purification after performing ablution (istinja'). And if performing ablution (istinja') is difficult, then we hope that acting upon the opinion of the Malikis will be accommodating for you.

As for undergoing surgery, its non-obligation is the preponderant opinion.