It's also important to note their correct forms as used in real life, because they are not all the same in construction.
* 같다 is an adjective, so 같습니다, 같다, 같아(요) (같는다 doesn't exist).
* 보이다 is a verb (in passive voice), so 보입니다, 보인다, 보여(요) are possible. '보이다' is the dictionary form which (almost) never appears in real usage.
* 모양이다 is made of 모양(n) + 이다(special particle). The whole phrase acts like an adjective.
* 보다 in '~나 보다' is an (auxiliary) adjective, so only 봅니다, 보다, 봐(요) are possible. The verb conjugation form 본다 is not possible. For example, it's 비가 오나 보다, not 비가 오나 본다. The latter has an entirely different meaning.