Lifting & Weigh Loss

You can't sopt reduce so who knows when you'll lose your belly? But I'd suggest taking measurements and logging every 2 weeks or so to notice changes in body composition, so measure hips, waist, neck, arms and legs (relaxed) as well as bust.

As for running and lifting going against one another...One compliments teh other to some degree, more muscle will help with decreasing running injuries, give you more power, help with fat loss so help move you faster and give your circulatory system a workout and as your cardio improve you'll be more efficient in general.

I know plenty of runners who lift, I'd strongly suggest not doing both on the same day however but if you MUST run on a lifting day lift first and run a few hours later to give yourself a chance to recover. Reason being that most, if not a good chunk of your glycogen will be used up so when you go out for that run your body will need to recruit some fat for fuel.

Also, I've thought about doing C25K (Couch to 5k) because I feel running at least one day a week, (ideally 3) would help with my weight loss but I've read and been told lifting and running long distance go against each other.

CV and resistance training are complementary. Personally I run five times a week and do two resistance sessions.

CV improves endurance, resistance helps my running form and reduces injury risk.

If you use a structured running programme like C25K keep it at 3 sessions PW as its a progressive plan. If you don't build you won't get the benefits.

In terms of session planning, the effect of glycogen depletion impacts on your form. Both disciplines need good form but generally resistance isn't going to deplete as much energy as running will, once you're through the first half of the programme.

There's no problem with lifting and then running right afterward.

The only time cardio and lifting aren't both recommended is if you're trying to gain weight, and that's only because the cardio burns extra calories, so you'd need to eat extra calories on top of your surplus to make up for the extra burn. Since you're not trying to gain, go for the extra cardio!

So its okay to lift then go run immediately after? I know its not ideal but it won't hurt. Correct?

No reason not to, the only thing is running form is quite sensitive to fatigue, but if you avoid your leg days then that should be ok.