Meaning of 一样 in 你要像喜欢甜一样喜欢苦
你要像喜欢甜一样喜欢苦
  
  (1) What does 一样 means in this sentence?


"像 (X)一样" means "the same as (X) "  or "like (X)" in this sentence


你要喜欢苦 = You have to love bitter
你要[像喜欢甜一样]喜欢苦 = You have to love bitter [the same as you love sweet] /  You have to love bitter [like you love sweet]


[像喜欢甜一样] is an adverbial phrase that modify the verb phrase 喜欢苦


  2) Can I put VERBS following 一样?


My answer to (1) said you can,  because [像 X 一样 ] = [the same as X], and the following sentence can be a verb phrase or adjectival phrase E.g.  "像 Mary 一样去當護士了" or "像 Mary 一样漂亮"