The both sentences have the same structure.
First one: 男朋友是那个觉得逗哭你再慢慢哄会很有趣的朋友
男朋友是朋友,is the main clause,which can means : boy friend is the friend
“那个觉得逗哭你再慢慢哄会很有趣的” is the adjective modifies the noun”朋友” can be translated: who think it is funny to teases you until you cry, and cheer you up later
So connect them together we can get: boy friend is the friend/one who think it is funny to teases you cry, and cheer you up later
Second two: 男朋友是那个看到杰西一卡。阿尔芭会流口水但还是会对你说“比起你来她算个啥”的朋友。
男朋友是朋友,is the main clause means : boy friend is the friend
那个看到杰西一卡。阿尔芭会流口水但还是会对你说“比起你来她算个啥” ” it is the adjective modifies the noun”朋友”
Even though he will be drooled over Jessica Alba, but for him, you are the most beautiful in the heart, and no one can be compared with you.
Here we get the meaning: : boy friend is the friend/one be drooled over Jessica Alba, but for him, you are the most beautiful in the heart, and no one can be compared with you.