exercise help/tips?

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I'm in africa for a few months with work and have decided to use the opportunity to lose a bit of belly and improve my fitness having put on about 10kg in the last year due to poor diet and lack of exercise when travelling.

So far i have:

- Cut out booze completely. Tbh i don't drunk much usually but its the norm on extended trips that sitting in the bar is the main past time. Its making my evenings harder to pass but will be worthwhile in the long run.

- Minimized carbs. My usual approach to Africa is only to eat it if its been bbq'd or fried but i'm trying to do better whilst hoping that doesn't result in the usual stomach carnage.

Breakfast is omelette & fruit. lunch is salad, evening meal is meat and salad/veg. I don't trust the fish as we are too far from the sea. Once a week i have to eat something more interesting so i will go to the Indian but avoid rice and naan [i will have a dosa though]. Tbh the food options are limited which is making the diet aspect harder that it needs to be. Snacks are yoghurt or a cereal bar, drinks are either water or cold infused fruit tea.

- Started jogging. For the last 2 weeks I've been working my way up steadily and now managing just over 5km every other day, best time around 35mins. I'm wondering whether to focus on bringing this down sub 30mins and increasing frequency to every day, or to keep to every other day and push the distance. By the time i leave [December] i want to be able to manage 10km in around an hour.

- Started following basic yoga vids on youtube to improve flexibility. I'll do 20-30mins of this before bed.

Now, for advice:

- I have been suffering from pain in my achilles for the latter half of the year, I guess due to piling on the pounds. I'm not having much trouble with it when running [I bought a pair of nike zoom all out for their generous heel cushioning] but first thing on a morning my heels feel stiff and tender [not the heel pad, the achilles and lower calf]. Sometimes there is no pain at all, other days i walk like a pregnant penguin. Any tips of how to combat this?

- Is there a weight-free routine I can follow to improve strength and burn fat? The hotel 'gym' is woeful with no weight equipment at all. I understand weight training will help burn fat quicker but i might struggle to find a gym i can use within walking distance.

Any other tips?

I was cycling 40km 3 times a week before I came here so its not like I was completely couch bound. I don't expect miracles but it'd be nice to drop a few kgs and raise my general standard of fitness so I can enjoy it and therefore continue the trend when I get home. I'm miles away from anything remotely touristy so happy to devote as much of my spare time to this as required, there is literally nothing else to do around here other than drink.