Learn English – As well as + verb-ing

Nowadays is a complex temporal adverb that means much the same thing as Positive anymore.
That is, Nowadays, S asserts that S is true at the present time,
and also presupposes that there was a time in the past when S was false.

• Nowadays, everybody carries a phone.
• Everybody carries a phone nowadays.
• *%Any more, everybody carries a phone. *
• *%Everybody carries a phone any more. *
  (The '%' in front of the sentence means it's dialectal -- see the link for details)

This is the opposite of normal any more -- which is a Negative Polarity Item
and therefore can appear only in a negative clause.
Normally, Not S any more asserts that S is false in the present,
and presupposes that S was true in the past.

• Nobody wears a fedora any more.
• Nobody wears a fedora nowadays.

But the reason why the second sentence is preferable to the first has nothing to do with nowadays.
Start is an active inchoative predicate, and therefore its use in the present tense
is interpreted in a Generic sense. With a punctual predicate like start,
that would mean a repetitive sense, as in

• The motor starts to sputter every time I press the accelerator.

That is, the "present tense" starts to get is not used to refer to the present time;
the progressive is starting to is used instead.

We should distinguish between different lexical meanings of each word, since each meaning will have different grammatical and semantic requirements. Based on my own understanding, for the basic meaning of "speak" and "talk", "speak" refers to the actual act of saying something, and corresponds to the intransitive version of "say", whereas "talk" refers to the act of engaging in communication with others. This difference explains many of your examples, but not all, since some appear to arise due to different lexical meanings.

Examples of the distinction between basic "speak" and "talk"

• "speak up", "speak out", "speak clearly", "speak confidently/authoritatively": These show that "speak" has to do with the act of saying something.

• "actions speak louder than words", "speaks to the heart", "the clock spoke": Similarly these refer to things figuratively saying something. "talk" would be inappropriate here because these things are not having any conversation.

• "speak for everyone": This refers to being a representative voice, so "talk" doesn't work.

• "grammatically speaking", "so to speak", "speaking of", "talking about": "speak" refers to the actual verbalization, hence "speaking of X", while "talk" refers to the communication, hence "talking about X".

• "talkative": It means "like to talk" or "talks a lot", which is about communicating with others.

• "speak to", "talk to": Usually there is hardly a difference, but the distinction becomes clearer in certain situations. Anyone can "speak to the king" if given the opportunity, but to "talk to the king" suggests further that it is a conversation and not just one-way. In contrast, "speak with" conveys the sense of both speaking to one another, so I doubt it is distinguished from "talk with" in actual usage.

• "spoke about X", "talked about X": "spoke about X" conveys just the speaking, while "talked about X" conveys speaking to others. But for this example both convey the same thing when taken in context.

A few examples of other lexical meanings

• "spoke wise words", "speak English", "speak the truth": It is a different meaning of "speak" that is transitive. Nevertheless, there seems to be still a relation to the above distinction. We can say "talked to them in words of wisdom" and "talk to them in English".

• "I'm talking grammar here": A transitive meaning of "talk". This can be used in place of "grammatically speaking", but conveys talking to the audience about grammar rather than simply stating something.

• "give a talk", "give a speech": The noun "talk" just happens to be spelt the same as the verb.

By the way, I just found out that http://www.thefreedictionary.com/speak mentions roughly the same distinction as I did, but I disagree with what it says about telephone calls. I don't think there is anything wrong with asking to talk to someone on the phone. I don't even think it is less formal today.