I tend to split infinitives, it seems more correct to me sometimes, not proud. And I sometimes start sentences with prepositions. Seems fluid to me most times.
The thing I do recently that I hate the most is to make sentences like the following. I write sentences like this now because everyone else does it?
That almost infuriated me when I first saw it. That’s a DECLARATIVE statement, not a question!
I have worked as an English grammar teacher and I have a Master’s Degree in Linguistics. And I can still never use ‘lay’ and ‘lie’ correctly!
Psst, check your OP for typos. 
Do you mean that you don’t always know which to use, or that you sometimes use the wrong one even though you know better?
Heh! I tripped over that recently. Fortunately, a friendly reader spotted it in time.
To tell the hellish truth, I don’t really grok all the rules about “I” and “me” and “who” and “whom.” The whole object/subject thing is messy.
The one that gets me in the most trouble is just carelessness. “She was painted from the waist up with beautiful eyes and glowing hair.” Um… She has hair and eyes from the waist up? Odd-lookin’ dame…
OP should know that there is nothing wrong with starting sentences with prepositions. But conjunctions are a horse of another colour. 
IMHO it is OK to intentionally split infinitives.
Quite seriously: I gather that grammarians nowadays are pretty much in agreement, that there is nothing wrong with infinitive-splitting. The old prohibition of it was basically a “nonsense” rule, sold as a bill of goods to the world by old-time grammarians and teachers. The no-split-infinitives thing was a function of the attempt by these folk, to make English grammar conform to the rules of Latin grammar; which as somebody said, makes about as much sense as trying to play baseball according to the rules of football.
At times, for sure, avoiding the splitting of an infinitive results in very stilted wording, whatever way you do it.
I went back to using split infinitives with abandon when I realized I was losing the rhythm of “hill talk.” Other grammar rules had to go out the window, too.
The few times I’ve ever needed to use “whom”, I know it’s not “me” and I change the sentence. 
I will reread something and see that I’ve strung 4-5 independent clauses together with an unholy mix of colons and semi-colons.
The OP’s first two examples aren’t as “carved in stone” as they once were. But the third? Why would you treat it as anything other than a simple declarative sentence. Perhaps another example would clarify.
Too many commas, and run on sentences. It works okay for me in speaking, but, for instance, when posting here, I tend to casually imitate, those very speech patterns, and often, it doesn’t quite come off, the way it ought.
If you take my point.
I often deliberately end my sentences with a preposition because otherwise it comes across as old-fashioned or pretentious.
“Who are you speaking to?”
vs.
“To whom are you speaking?”
Occasionally, I’ll let a “your/you’re” mistake slide in.
In the Importance of Being Earnest, Lady Bracknell says at one point, “[T]hat’s a very good age to be married at.” If preposition stranding is ok by her, it’s ok by me.
Usually when a declarative sentence ends with a question mark, it implies a further question. “I tried what you said to do but it didn’t work? [Did I do it wrong?]”. “Well, I’m out of ideas? [Do you have any?]” and so on.
As for me, there are no grammatical mistakes that I make on a regular basis as if I’m making them frequently they cannot perforce be a grammatical mistake. They may be an orthographic error or a punctuation mistake but they’re not ungrammatical.
Why do people write questions without question marks?
“Why would you treat it as anything other than a simple declarative sentence.”
Professional writer/editor who checks any clause that starts "there’s a … " because the odds are very good that it should be “there are,” not “there is.” There’s a lot of different ways this pops up.
For me it’s using object pronouns after “than,” instead of subject pronouns. I know it’s wrong, but it sounds right to me, and I can’t help doing it. Stopping would take someone stronger than me. (ok, ok, stronger than I!)
From the OP:
Comma splices and sentence fragments are always quite popular.
I had an English Composition teacher who always exhorted us never to begin a sentence with “There” (never mind if it was “There is” or “There are”), on the theory that there was always a better and clearer way to say whatever the sentence was trying to say. I can’t imagine what she would have though of a sentence like “There’s no there there”.
Ending sentences with prepositions is something up with which I shall not put! :mad:
ETA: Incidentally, if you wanted to be pedantic, as I apparently do now, the error in the first isn’t so much the ending preposition as it is the incorrect case of the pronoun. “Whom are you speaking to?” is, as I understand it, perfectly correct.
I’m pretty sure that I’ve split some infinitives, because I don’t know what they are.
I don’t use “whom” correctly because, like others, “whom” sounds pretentious so I don’t like to use it – ever. In the preceding sentence, “like others” should probably have been “as others have said” or maybe even “like other words”. So there’s that kind of mistake too – not sure what it’s called. Maybe just lack of clarity.
I’m also pretty confident that I misuse hyphens/dashes.
I mix and misuse verb tenses. I have a lot of trouble with “had” before a verb.
I write sentences that are too long.
I use wishy-washy qualifiers like “probably”, “really”, “pretty” and “maybe”. I probably use “like” when I should use “such as”. “Such as” sounds a teensy bit pedantic.
I start too many sentences with “I”. Not grammatical so much as lazy style. Should that have been “so” much or “as” much? Who the hell knows. 