Learn English – One subject with multiple verbs

In English, two verbs that refer to the same grammatical subject are normally connected with "and", and the two example sentences in your question are correct.

(I consider these sentences as examples of American English. In British English, there is usually no comma before "and", but see also Commas, subject and verb on English Language & Usage SE.)

There are languages that use "and" less frequently (e.g. 和 in Standard Chinese), but if you left out "and" in the first sentence, a native speaker of English would normally feel that the sentence is incomplete until you add "and [x]".

Gerund v. Participle

I think you're confusing gerunds and participles. While they look the same (note: in Old English, they were different), they function entirely differently.

The first set of -ing words you give are not gerunds, but participles. These are verbal adjectives that modify a noun or pronoun.

Gerunds, however, are verbal nouns. They do not modify other nouns or pronouns.

Make and Have

For make, you use an accusative plus infinitive without "to". All of your examples are correct. It's she made me do it— no participles needed!

For have, the sentences are actually awkward English. It would be better to switch it around:

1. The system has always been unbalanced.

2. She's been happy this whole year.