Can you catch hiv or any infection with gloves on? or after removing gloves? ?

Yes: If you have exposure of infected fluid to broken skin or mucosa, then yes, you can have infection spread. If you are just touching someone, with or without gloves, the chances of contracting HIV is extremely low. Now, your question of "any infection" is extremely vague and depends on infection; obviously, gloves are not going to help with tuberculosis.

Myth dispelled: Gloves are worn to protect from direct contact with body fluids. Hiv is transmitted through contact of blood, semen, or vaginal fluid. Hiv transmission from direct needle sticks are more likely than from HIV infected gloves. How do you remove your gloves? Please wash your hands thoroughly after removal of those gloves. Skin is the natural barrier. So make sure your hands are not dry or chapped.