"Come, sit, eat and go."
Translation:आओ, बैठो, खाओ और जाओ।
Not exactly irregular.
बैठ ('baiṭh') has a consonant ending due to schwa deletion (ie, the 'a' vowel attached to ठ is not pronounced). To make the तुम-form of the infinitive, we add ओ to this. Adding ओ to the vowel-less consonant ठ् would make it ठो, making the word बैठो.
Many verbs have a similar imperative form - देखो (see), सुनो (hear), सोचो (think), तैरो (swim), रहो (stay) etc
Yes. 'बैठ करो ' is wrong.
'करना' is usually used to make compound verbs out of nouns and adjectives (eg: पसंद करना - 'to like', गलती करना - 'to make a mistake', प्यार करना - 'to love' etc). It is not added to verbs.
An exception is the addition of 'करना' to verbs borrowed from foreign languages when you insert them into a Hindi sentence. Eg: You can say 'sit करो' instead of बैठो in Hinglish.