I'm still unsure what you want to join here. Perhaps you actually want to join two clauses or two adjectives, not two sentences. Please read this carefully if you don't know the difference between words, phrases, clauses, and sentences. The link is about English language but almost everything in the link can be applied to Japanese, too.
([×] I like languages, am interesting, and learn them a lot.)
This sentence is ungrammatical, but the problem is not about verb/adjective forms but about an inconsistent topic. This sentence tries to say these three things in parallel, right?
- 僕は言語が好きです。 I like languages.
- 言語は面白いです。 Languages are interesting.
- 僕は言語をたくさん学んでいます。 I learn languages a lot.
Each sentence makes perfect sense. But can you see the second sentence above has a different topic marked by は? In the first and third sentences you're talking about 僕, using 僕 as the topic. But the second sentence uses 言語 as the topic. Note that you cannot say [×]僕は言語が面白い; it's ungrammatical.
The sentence you made is ungrammatical because the first 僕は works as the topic throughout this sentence. The second part would sound as if you were saying 僕は面白い ("I am a funny person")!
There are many ways to fix this sentence.
I like languages and learn them a lot. Languages are interesting.
(Simple and clean: Split this into two sentences, and use only one topic per sentence.)
I like languages, and languages are interesting, and I learn them a lot.
(Explicitly switch the topic for each clause. It looks poorly written, but works)
I like languages and learn them a lot because languages are interesting.
(Here 言語は面白いから is a subordinate clause that adverbially modifies 学ぶ. This 言語は works as a "temporary" topic that is effective only in this subordinate clause. The topic of 学んで is 僕 again.)
I like languages. I learn languages a lot because they are interesting.
(Almost the same as above. から introduces a subordinate clause, which means you can have a different temporary topic in that clause. The main topic of the second sentence is still 僕, which is omitted.)
However I don't know what your teacher wanted to mean by saying "plain form". Usually the plain form cannot be used on its own to connect two things inside one sentence. Maybe your teacher wanted you to split this sentence into two? Or if you presented this sentence orally to your teacher, maybe your teacher took it as two sentences (i.e., there are two periods) and said "A sentence must not end with a te-form".
(楽しくてら is obviously a typo.) These are all valid because エレクトロニクス can safely work as the topic of the three predicates (面白い, 楽しい and 一番好きな科目だ) here. The third line consists of two sentences, and the first sentence ends with a plain-form.