Heart rate

Base it on how you feel. The formula that estimates max HR is very inaccurate. It says mine should be about 181 I think. But, I know it's really somewhere around 205 (based on how high I've seen my HR get during races and how I feel when it does - over 200 and I feel bad so I know that's getting quite close to my max).

When I run, my average HR is 150 to 167 depending on my pace for that day. But, my max during the workout can be up to 185ish (or even more on a hotter day). It's not dangerous as long as your Dr states you're in good health. You'll feel bad if it truly starts getting too high

ETA: My resting HR is anywhere from 48 to 62 depending on the day, with the majority of the time, being in the 50's somewhere. The more miles you run to build up your aerobic base, the less your HR will spike, but I don't think the levels you're talking about are dangerous at all - at least they wouldn't make me bat an eye.

I'm no medical professional but you're probably fine. I think the recommendation is 90% of MHR max for high intensity exercises so if it's freaking you out, then slow down when you get around 170bpm. In my experience a spike that that is fairly common especially doing something high intensity like running hills. Also, that calculation (220-age) is just a guesstimate so don't put too much behind it. The only accurate way to get your true MHR is via stress test. My MHR is supposedly 180 and I tend to get pretty close to that during high intensity intervals.

However, I will say if you start to experience any symptoms like premature exhaustion, rapid heart beat, nausea, dizziness, etc, you should back off and probably also talk to your doc.

The best person the address this is Phil Maffetone. Google him, or just "MAF run". Even experienced runners struggle to keep their HR under a Zone 2 rate at first. Even though I could run well over an hour in Zone 3, I had to walk hills to stay under 130 on a hot day. Once I adapted, my slow pace became faster than my previous fast pace. It actually takes a bite out of your pride to be able to do 5 miles at 8:00 pace, and have to slow to 10:00 to keep it under the target. There's too much detail to post it here, but read up on MAF and you'll learn a lot.
I believe you should only run in two zones: 2 or 4. "Runners high" is zone 3, because your body is burning sugar and it feels great. You feel like you've done something. But there is a trend in the fitness community to become "fat adapted" which is where you train your body to burn fat as fuel. This happens in Zone 2, and if you go over, you switch to carb burning, and get tired far faster. You have enough energy in your body to run a half marathon without needing to eat anything. The reason you took three hours wasn't a lack of cardio, but of muscle strength. I'm trained in CrossFit Endurance, and my opinion is that you would greatly improve with a combination of squats for strength, mileage at MAF pace, and some intervals each week. It all depends on your goals. The only real downside of MAF is the amount of time it takes. I believe your friend is correct, and humbly suggest that your heart rate monitor should be respected. I broke 3 hours in a marathon by staying in the correct zone. But it took a long time for 6:50 pace to be below my threshold. If I had just gone in the Happy Zone everyday, there's no way I could have done that.
If you just want to jog everyday at the same pace forever, then do that. The body gets used to routine and will plateau. Or, you can mix it up and improve.
Michael

My heart rate is very similar while running! I was training for a race in the Mississippi humid summer... whoa! I think I remember mine spiking above 190.

If you like science, Phil is definitely going to excite you. But also keep in mind that this is a huge world, with lots of variation to get it done. If you have follow-up questions, feel free to send me a PM.
2 things to additionally consider:
every extra 10 pounds increases your chance of running injury by about 15%
every extra 10 pounds slows your average pace by a min per mile.
These are REALLY general, but the concept is that if you are starting heavy, or without a running background, ease into it with walking and cycling (not weight bearing). If you struggle to go slow enough to stay at the correct HR, it's perfectly fine to use the Higdon method of 5 min jog, 1 min walk. I prefer to use the HR to tell me when/if I need to walk, rather than a specific time.
Also, it takes VERY little speedwork to really see an improvement, but it is harder on your body and it's recommended to get a solid foundation prior to adding intervals. If I was building your schedule, and you currently did a 5 miler every day at 10:00 pace, I could modify it to this:
4 days of 45-60 min (notice I use TIME, not DISTANCE) at MAF HR, regardless of the pace
1 day of 4-6 quarter mile repeats at the fast pace that you can do them all at the same time (which will take a few weeks to figure out). This day would be much shorter time-wise, but probably the most significant to your improvement.
If I had to summarize the biggest benefit to MAF, it would be that you go slow enough to be able to be consistent without getting hurt while your body adapts to the increases in activity. If you are too tired to go today, then you went too far or fast yesterday.

Michael