Beware is a lexical verb, but uniquely in English for a lexical verb, it is a defective verb. "Beware" is usually used as an imperative, e.g. "Beware of the dog". It can be used as an infinitive, particularly after a modal verb, e.g. "you should beware of danger". Other forms often start to feel grammatically weird.
It is a compound verb with "be" as its head (contrast "become" where "come" is the head and that works fine). Given how irregular "be" is, this probably the source of all the grammatical weirdness. Indeed, copular be with the adjective "wary", i.e. "to be wary" seems to be used instead. In that case, "beware" is generally preferred to "be wary" in the imperative, otherwise "be wary" is preferred.
Although Wikipedia lists it as an irregular verb, it does not have irregular forms, and therefore by default should be considered regular. Some older, or poetic texts, may use forms such as "bewaring", "bewared", "bewore", "bewarn"/"beworn", etc. But for teaching purposes these are probably best ignored.
Some speakers may use "beware" as an adjective, e.g. "please be beware of the danger". While probably acceptable in speech, it would be better to say, and definitely better to write, e.g. "please beware..." or "please be aware..." or "please be wary..."
- at least we can't think of any others
- Julius Caesar Act 1, scene 2, 15–19,
- For a written example see https://books.google.com.hk/books?id=4Q1qe21qLQoC&pg=PA207&dq=%22be+beware%22&hl=en&sa=X&ved=0ahUKEwji5OSspqzlAhXSE4gKHYujDu4Q6AEIMDAB#v=onepage&q=%22be%20beware%22%20adjective&f=false