Is it permissible for a woman always to perform ablution and place a barrier to prevent discharges from exiting, then pray with that ablution more than one prayer and for long periods?

These discharges invalidate ablution according to the general consensus of scholars. Even though they are pure, there is no need to perform istinja (washing the private parts) from them. Ablution is invalidated when these discharges exit to the outer part of the vulva, which is what becomes visible when a woman squats for her needs. It is not a condition for the discharges to exit completely outside the vulva. Placing a tissue does not prevent the invalidation of ablution if the discharges reach the outer vulva.

If you are afflicted with sals (incontinence) such that the discharge does not stop for a duration sufficient to perform purification and prayer, then according to the majority of scholars, you must perform ablution for each prayer after its time has begun. You then pray the obligatory prayer and any voluntary prayers you wish with this ablution until that time expires. The Maliki school of thought holds that a person afflicted with sals is not required to perform ablution for every prayer; rather, their ablution suffices as long as they do not incur another hadath (ritual impurity).