You can put two independent clauses together with a comma. There is nothing wrong with that. When they talk about too many commas, they usually mean more than two clauses separated only by commas. The above sentence could have been written as: I was so determined to learn that I hired a tutor who started with a 90--minute lesson. Notice that 'that' is substituted for the comma. Also, some dependent clauses could be strung together: "I got up out bed, brushed my teeth, took a shower, had breakfast and started of for work." This is legitimate, as the complete thought involved short dependent clauses that have to do with what I did to get to work. This would not be acceptable: "I got out of bed, when I noticed the sun out, I looked out the window, out on the lawn I noticed a man standing." Here, the phrases were longer and not as closely connected. The commas detracted from the understanding. Hope this helps.

No, it is not right to connect two sentences with a comma. Your example does not do that. "I was so determined to learn" is not a complete sentence, in the way it is used in this case. It needs "that", followed by another clause, but a comma can substitute for "that". A similar case would be, "She was such a fast runner, she ran to work faster than the bus would take her there."

A teacher could probably explain this better, but it looks to me like you don't really have two independent sentences/clauses. "I hired a tutor..." is the weaker (or dependent) clause which depends on the first clause, and there is an understood "that" before this second dependent clause. "I was so determined to learn (that) I hired a tutor...." That's my non-professional evaluation.

A comma can be used to mark where a pause would be if the sentence was spoken. Newspapers are informal media (more casual than print books or textbooks) and it is characteristic of that genre of writing to be less precise about punctuation. IMHO.

Just wanted to pipe in and say that "rules" about usage don't apply equally to written English and spoken English. There is a huge divide between prescriptive grammar (that tells how language should be used) and descriptive grammar (that describes how language is actually used). As well, there is a continuum of rightness -- some things are rule-governed (third person s) but a lot of grammar is sliding scale ... it depends on context and speakers' intention. It's always been important to make determinations about "correctness" based on 1) the context (what's going on), and 2) the medium (e.g. spoken conversation between two people vs a written text that is one author to hundreds of readers) A huge difference between speaking and writing is the that writing is asynchronous (written at one time, and read/heard much later, with no chance for reader to ask questions/interact with the writer) whereas speaking is a dynamic real time process. Especially as English gets "owned" by fluent but non native speakers, the whole idea of abstract "correctness" is really going down the toilet. It's about communicating with finesse and coherence over a whole conversation -- everyone misunderstands; sometimes due to grammar mistakes, sometimes due to hearing wrong, sometimes due to just not paying attention... This focus on "correctness" is something that rule and accuracy-focused Asian learners often bring to their experience of language learning. IMHO.