I think this comes to the heart of trying to see so much with so few days available. I would prefer two days in Mahabalipuram.

Kanchipuram is a hectic Indian town; Mamallapuram (Mahabalipuram) is a much smaller and more relaxed affair. The temples in Mahabs are World Heritage Listed and the registered monuments include rock relief carvings. The temples in Kanchi include important current pilgrimage destinations.

The other consideration is the open times of the temples - the 5 main / popular temples in Kanchi are each closed between 12:00pm and 4:00pm (one of them may open at 3:00 - I forget which). That said, if you want to squeeze Kanchi in then you can.

There should be a bus between Mahabs and Kanchi; although equally you can take a car which gives you some flexibility. There are local trains from Kanchi to Chennai:
https://erail.in/trains-between-stations/kanchipuram-CJ/chennai-egmore-MS

The centre of Goma is safe for walking during the day time but at night it is better to avoid walking. You can take pictures but I would recommend taking them with a smartphone and not a big reflex camera. Traffic is busy in Goma, so just keep an eye out for motorbikes coming from all directions when you're walking.
In terms of sim card you could either go with vodacom or orange. Price-wise there's hardly any difference and they both offer good coverage.
Boats go regularly from Goma to Bukavu and back, at least twice a day so there shouldn't be any issues. If you can try to go on the morning one (at around 7) to enjoy the scenery.
There's taxis in Bukavu. However, I would recommend to contact your hotel beforehand and they can send you the number of a trusted driver. A ride will be about 5USD.

It is NO LONGER necessary to register your phone on arrival at the airport.
This was cancelled shortly after Dr Abiy became Prime Minister.

ETC now sell SIM cards at a stall in Term 2 arrivals. BUT it only opens at 08.00
It is a long table with several PC units on it. Once in the public arrivals hall after customs, turn left and roughly where Yellow Spot cafe was but on the right in front of the windows you will see it. .
I imagine they sell top up cards as well

I just heard the SIM card is 119 now is it true?

@fharrison881.675654 so can you share your experience if you managed to find a telcel shop in Cancun airport because I will be arriving there too?

Hi,
I have just left Zimbabwe after 2 weeks around although I didn't visit Harare.
We have changed in small shops (all of them accept ecocash so there were possibilities to get ecocash) and asking people.
The change for bond (physical notes) is 7 for 1 US dollar. For ecocash is around 9.2 for 1 US. We have changed mainly ecocash. We got a sim card enable with ecocash in an Econet agency without problems.

You can have an idea on how it evolves daily here:
https://zimbollar.co.zw/

Does anybody know, if there follow negative effects or any other consequences for the writer from a invitation letter? Maybe questions from the goverment/the police or so?

Last year, our host gave his number as reference as needed when buying a new sim card. He was later called and asked who I am and how he'd know me. Scared him enough to ask me to destroy the card as soon as I'd left the country ...

I also know a Pakistani guy who was questioned (and his father, too!) about their relationship to a guest who gave their address on the form when they entered the country (from India, which probably didn't help ...).

So I'd say chances are high the name shows up on some lists - and depending on who looks at it, could put them on the spot. Honestly, I'd rather pay an agency then risk getting a friendly stranger in trouble, it that's an option.

Just think, maybe it just prompts some security person to check the inviters social media accounts, and they find something they don't like, which would otherwise have gone unnoticed, and start making a big deal out of it ...

Do you think weariness tank tops is all right to wear around? Or is that not a good idea? Maybe not culturally acceptable for foreigners to wear that? However, researching the temperature in January, it’s like 5 to 15°. So maybe not tank top weather anyways.

The temperatures will be too cool for tank tops; and it won't be culturally respectful - and it will be problematic entering temples and mosques. Wear shirts.

And is it a really bad idea to hold your cell phone and walk with it and have headphones on? Earbuds or a big bulky ones?

Please don't do that. You want to connect with your surroundings, not be distracted by noises in your ears. Be alert to where you are. "Be here now."

I’ll do some research, but what is Connaught place?

https://www.lonelyplanet.com/india/delhi/attractions/connaught-place/a/poi-sig/386553/1342597

EDIT: Given the level of anxiety you seem to have about this, and that you have no real plan, I'm going to suggest you forget about Delhi and the north, and instead fly into Kochi and spend your time in Kerala. Much easier for first-time visitors to India.

Actually, if this is your first time travelling to India, I would not recommend doing it alone. I didn't see anything describing how experienced a traveler you are, but all it takes is getting sick, and you'll be really grateful for another person. If you are a very experienced solo traveler, go for it. Otherwise, tread carefully.