yeah, it use います (my mistake).What textbook are you using? Doesn't it say 店に客が三人います?
can I write '二枚パンツを買います' ?年が上（だ） means "older" as a set, i.e., ３つ modifies the entire clause 年が上, not just 年. You can't use の after the counter in these cases, as in ３センチ背が高い, ３キロ体重が重い or ３坪面積が広い.
FYI, 店に３人客がいます is also correct.