Is it permissible for someone who vowed to slaughter a sheep and give it away in charity to buy the slaughtered animal from an abattoir even though it is missing parts, and is it permissible for him to fulfill the vow in installments due to financial hardship?

The one who made the vow must slaughter the sheep they committed to, and buying a slaughtered sheep does not fulfill the vow. They are obligated to fulfill the vow whenever they are able. If they are permanently unable to fulfill it, then an expiation for a broken oath (kaffarat yamin) becomes incumbent upon them.