Singing high notes and straining

I can hit C4/D4 somewhat comfortably, and as I approach A4 the strain gets progressively worse to the point you cannot hear my voice if I try to go any higher. When i had the trial (i'll be purchasing a subscription soon) I was interested in head voice, extending range, etc.  anything that would help me to sing higher w/o the strain. However, on a lot of the excercises (on 30day singer, youtube, tutorials, etc), I can only follow along mid way until it passes my range, and leads to neck strain. I've also looked at the videos on vocal strain as well.

So my question is, am I supposed to not have any strain whatsoever as I practice to extend my range? especially at the edge my limitations? or do I go high until i feel some discomfort and then back off?
The other thing I'm also curious about is if you are able to sing high notes w/o straining, what happens when you get the highest note you can hit and then try to go beyond that, what prevents you from going any higher? 

Hi, Ep! I encourage you to make sure you're shifting registers when you start to feel strain. For example, as you approach A4, you probably need to start lightening and/or nasalizing your sound (to "mix" in some head voice coordination with your chest function). If that's not relieving the strain, it may be time to "flip" or "shift" into head voice. See if singing on a lip trill, MUM, HOO or another syllable helps you sing with more ease.

Here's a live lesson I did on strain & vocal health: https://www.youtube.com/watch?v=s6HRdzfpT20. 

As for singing higher, we're all eventually limited by the size/length of our vocal folds and the amount of space within our larynx for those folds to stretch. 

Thank you! that was a great video! didn't know there was a youtube channel too, will check that out more frequently.

So when I'm going higher up the range, I do try to do lip trills, mums, or hoos. once I start to pass a certain key, my neck progressively tenses up, my larynx shoots up (despite trying to imitate a yawn) and eventually cuts out.
I know your lessons are primarily for those with higher ranges, but it's ranges I would like to reach at some point. So even in the lesson with Head Voice, I could only follow along until my voice cut out or there's too much strain.
Thanks to you, I now understand that any strain is not good. So with that in mind, when i renew my subscription, i'd still like to specially work in improving head voice and extending my range.
Should I be going as high as I 'comfortably' can and then stop, and will doing so over a long period of time allow me to grow into the next key w/o strain? Is that the approach I should be taking? or is there something else that I can safely do, that will allow me to grow into those higher notes?

Great! Here's another live lesson you may enjoy, covering range extension within each register: https://www.youtube.com/watch?v=JXqiqTyxoBM&t=560s. 

One of the tips I give there is continuing with an exercise even if just air comes out; for example, singing the MUM 1358531 pattern, and if your sound cuts out on the 8 (highest pitch), that's okay. But if you're singing something like an EE or AH on a 12321 pattern and no sound is coming out, it's a good idea to stop. The rationale for continuing slightly past your "ceiling" is so that your vocal folds can stretch and approximate the desired pitch, even if phonation (sound-producing vibration) isn't happening. 

My favorite position for high head voice is an NG: the jaw is relaxed and mouth is open, but it's significantly easier than singing an open vowel. Experiment with that! 

It's also helpful to get an idea of how high your voice type typically sings. You're a person with a unique voice and range, but it can help to know what other basses, baritones, or tenors can be expected to sing. Here's an article I wrote on low voice types: https://www.30daysinger.com/blog/low-voice-types-bass-baritone-and-tenor-range.