So you've been to Tokyo? Perhaps it would be a better idea for you to tell us where you've been before so that the suggestions doesn't clash. Can only give suggestions for Tokyo so,

-> 4. Yes it will be a rushed trip but you can make limited stops rather than try to cramp all together. That will be more comfortable for your parents too.
-> 5. 100K yen per pair for all 7 days? It's a little tight but do-able.

You can do this simple calculation: 50k yen per pax/ 7 days.
- Per day spending: 7k yen including your transport around the place.
- Assuming you put aside 1.5k yen for transport per day, that's 5,500yen balance for food.
- Put aside another 500yen for misc fee: Meal @ 5,000yen per day.
- So play around with 5,000yen for your meals throughout the day. Per meal averagely you can afford to spend at 1,500yen. If you splurged your lunch and say, spent 2,500 yen, then your dinner budget has to be reduced.

Like you said not keen on shopping so perhaps that'll save you some money. But on the safe side, I'll suggest that you bring an additional 50k-100k yen as emergency cash/ backup in case overspend (you'll never know!).
1. Most of us here rarely change currency in Tokyo. In cases of emergency, you'll just have to go in any shop that offers the service without regard to the exchange rate.

2. You can check out HIS Travel http://www.his.com.my/pocket-wi-fi-rental/
Pocket WIFI rental at RM15 per day, very good rate. But usually pocket WIFI is used when there's more than 2 ppl for the trip so save cost.

But if you wish to get a SIM, try this instead. It's half of Celcom's rate: https://hello1010.my/country/asia/japan.html
Colleagues used their SIM and none of them encountered any issue.
You have 3 days in Tokyo right? Winter is cold and everything closes early, usually around 4pm -4.30pm similarly to autumn when I went. While you don't enjoy Tsukiji you'll still be going to bring your parents and partner to enjoy sushi? One of the days, you can do this like what I did:

Water Taxi from Asakusa -> get off at Hamarikyu Garden (enjoy the garden) -> walk to Tsukiji -> walk to Imperial Palace -> walk to Tokyo Station.

All the attractions above are quite near to each other, give or take 10-15min walk. 
Try the water taxi, it's really nice. You get to cruise along the Sumida River and enjoy sight seeing. It will be a pleasant experience for your parents.

Info: http://www.gotokyo.org/en/tourists/info/access/access5.html
You can buy the tickets at the counter. Just check the timing and make sure you're at the counter 15-20min before departure time to purchase the tickets.

There's more to see in Tokyo Station - there are souvenir shops, Pokemon store, Kit Kat shop etc. Also make sure you take a look at the station from outside. It's beautiful, even more so at night. 

In February - you may be able to see the Ume (plum) flower blossom. This will be a nice experience because Ume is said to be most delicate flower and it symbolizes protection and health.

Other places I will recommend:
- Ginza & Odaiba (it's closer when you get to Odaiba from Ginza); go to Ginza on a weekend and it's a pedestrian's heaven from 12 noon as the main street is closed off for only pedestrians to walk.

- Hakone: Yes but I'm not sure about February. Since it's winter, it may be too foggy to see Mt. Fuji. But, it may snow in Hakone and you'll see a different side to the place. I did a one-day short trip to Hakone, it's expensive and we only managed to do 3 things there... however if you plan it well and everyone could get up early for the train ride, it'll be good.

- Tokyo Tower - Sengakuji - Nakano - Ueno : you can do it in this order, or mix it around depending on where is nearer to you. Tokyo Tower - to be honest, it's nothing much on the inside except for some restaurants, souvenir shops, observatory and One Piece Tower.

If you want Observatory, i'd recommend the Metropolitan Government Building where it's FOC. But still, Tokyo Tower is iconic as it represents Tokyo. There's a temple nearby Tokyo Tower and it's the Zojoji. You can actually see the tower from the temple, and also a nice spot to take photos.

Sengakuji - you can opt not to go. I visited it since I was already in the area. It's of historical value and if you watch 47 Ronin, the story is adapted from the actual history. You can also read about it so that the visit is more meaningful.

Lastly, Nakano is a shopping area and while you're not into shopping, do consider your parents and the rest a good trip has a combination of itinerary for everyone. It's a really nice place with a lot of eateries. Nakano Broadway has a lot of shops with figurines, toys, books etc. If it doesn't interest you, perhaps just one round at the place and you can leave. The street is more interesting.

Ueno is famous for its park but since the day ends early, see how it fits into your schedule. If its almost night time when you arrived, make your way to Ameyoko Street for some street shopping/ eatery.
Since you're in Asakusa, if your mum are into kitchenwares, you can consider going to Tokyo Kappabashi shopping street - it's the place where they sell everything related to kitchen - be it knives, pots, pans, deco, fridges, utensils etc. It's nearby Asakusa, approximately 10-15min walk from Sensoji.

http://www.japan-guide.com/e/e3020.html

Sunsets and sunrise you can always Google: http://www.sunrise-and-sunset.com/en/sun/j...o/2017/february

if u wan to marathon traveling... u can goto europe... 10 country in 10days