Weights before cardio because in general weight lifting will be done much better on carbs, use them up and get you into the fat burning zone for your cardio.
However, people used to go and spend 3 hours doing silly weights in the gym, now people do 40mins to an hour because , by differing amounts in different people testosterone levels drops quite significantly after say on average 45 minutes.. lots of people keep weights toa minimum 30-45mins 2-3 times a week working on specific body parts only so you only do each muscle group once a week giving them time to build properly, then do cardio on different days, or just a completely different time, so isolating the two types of exercise from each other.
To the OP specifically, mirror work isn't always the best method, a tape measure can help, a combo of a bunch of things can help you see how your body is changing. Stomach/moobs/bum are often things on men that will be last to decrease in size, upper arms, thighs, neck, wrist/ankle are the things that are likely to be reducing in size first and the changes can be slight enough to not see in a mirror. Not seeing the stomach/moobs reducing in size(though judging by your weight they aren't likely to be big anyway) can kill motivation, but knowing you're losing inch's elsewhere can help.
cardio/weights/cardio/weights/cardio/weights spreading the weights out isn't great for the weights part of it, though if you're not looking to bulk up much its not the worst thing for you. The other problem is beginner gains in muscle building. If you've gone from almost no exercise to some, you'll find you can put on muscle pretty ridiculously easily and this can certainly account for lack of weight loss, though hopefully the thighs, biceps, ankles, wrist and neck will still lose inches to let you know weight hasn't changed but body shape has.
Cardio essentially burns calories on the spot, not that many tbh, the amount you burn in one hour of cardio is nothing compared to the 23 hours you aren't working out so thats the key, getting metabolism up during those 23 other hours. Weight training pumps metabolism up for the other 23 hours, and infact for more than that, Type 2 muscle is the muscle you want to be building/using for real metabolic increase which in turn helps you burn a lot more energy throughout the day which is why weights are actually better for losing weight than cardio. In general a good mix isn't half bad because cardio, and increasing your endurance and stamina burns some calories but makes you better able to do sustained form keeping weight workouts.
Eating after the gym is a subject with many opinions and depends completely on what you are doing. If you just did cardio, eating straight away, not at a normally schedualled meal is really counterproductive, cardio for the sake of burning calories is silly if you just go and eat those calories right back.
A protein shake/based meal from 10minutes to an hour after doing weights is supposed to be very useful for kick starting the rebuilding process and as building that type 2 muscle is what will help you burn more calories, and your body will use energy to build that muscle aswell as protein, its something you should be doing.
Last question to OP would be, what do you have for that lunch. THe optimum setup for weight loss is to not have a main meal or a large meal, just literally as many small meals as physically possible for you spread equally throughout the day with similar calories in each adding up to a slight calorie deficit for you.
Either way, diet is the key here, not exercise, weights, cardio are a very small part of losing weight, its 80-90% about how and what you eat.
