Is what I do, changing clothes and performing Wudu when I feel drops exiting after urinating, considered correct? And is it permissible for me to pray while sitting to make up for accumulated obligatory prayers due to joint pain that makes me too lazy to perform them standing?

The criterion for urinary incontinence is that if there is enough time to perform the prayer with a valid purification, one must wait for it. However, if the incontinence is continuous all the time, or if the time of its cessation is unknown, then one should perform ablution for each prayer after its time has begun and pray the obligatory and supererogatory prayers. If the incontinence affects the worshipper when standing but not when sitting, then he should pray sitting. As for a worshipper who is unable to make up missed prayers due to pain that afflicts him and harms his body, he may wait until the pain subsides, because making up missed prayers is an immediate obligation, provided it does not harm the body or livelihood.