Q&A: Choosing the Right Princess Cut Diamond for a Vintage-Like Engagement Ring for $3,000-$4,000 Budget

Hi, I wanted to start by saying I really appreciate all that you have done with this site as I have learned so much during my search for an engagement ring. I have visited local jewelers and searched online for awhile and I am pretty sure that I have decided to go with James Allen. I have a few questions regarding information that I was not able to find (sorry in advance if it is somewhere on your site). For any links I have also included the SKU to search easily in case they do not work. Here is some basic information first in terms of what I am looking for:

Shape of Diamond: Princess
Budget: $3,000-$4,000 (I would be willing to go more but she says she doesn’t want me to spend too much on the ring and she just cares that I ask, also we are saving for a house)
Color of metal: 14k White Gold
Setting: Vintage Style (with some sort of design on majority of ring) but could be either solitaire or three stone
Here is what I am heavily leaning towards for the setting (with princess cut center stone) – SKU 1222W14:
https://www.jamesallen.com/engagement-rings/vintage/14k-white-gold-royal-antique-style-round-shaped-diamond-engagement-ring-item-17424?a_aid=dmnd1357

My first question is I don’t believe that carat fully translates into size but I was wondering if you could clarify it a little for me. My understanding is that each stone has different dimensions so for example (note sizes are not exact) a princess cut .5 carat diamond could have dimensions of 4.3mm x 4.3mm or 4.7mm x 4.7mm even though it has the same carat weight and characteristics. From an eye standpoint will that make a big difference? Here are the two stones I am considering right now:
SKU 229238 – https://www.jamesallen.com/loose-diamonds/princess-cut/0.58-carat-e-color-vs1-clarity-sku-229238?a_aid=dmnd1357
SKU 241918 – https://www.jamesallen.com/loose-diamonds/princess-cut/0.57-carat-g-color-vvs2-clarity-sku-241918?a_aid=dmnd1357
(Note both approximately 4.65mm)

For comparison purposes and my question here is a stone of almost the exact same quality but with smaller dimensions and that one even appears to have a small visible black mark on the face of the diamond but is priced more expensive:
SKU 43462 – https://www.jamesallen.com/loose-diamonds/princess-cut/0.57-carat-e-color-vs1-clarity-sku-43462?a_aid=dmnd1357
(Note approximately 4.4mm)

Please let me know what you think of the two stones I am looking at and if my reasoning is correct. Those two seem to be the same size as some that are even .7 or more carats.

My second question is a little subjective but I noticed an incremental jump once I hit .65 carats or so and above and wasn’t sure if it was really worth paying more for a stone that seems to me like it would be almost the same as those two for $1200? I think this will depends on the answer to my previous question.

Third question is much more subjective and relates more to the setting rather than the diamond which I am not sure if you get as many questions about this. She really likes the vintage style look and I know one of the particular brands she likes is Veraggio. I happen to have a local jeweler here that sells them and while they look good online I was not impressed with how flimsy and dull they appeared when I actually saw them in person(even under jewelery store light) and how in actual size the design isn’t as clean looking and noticeable, especially for the price point. So with that I am leaning towards the setting on James Allen that I attached above as I feel it is a vintage style and still is a look she would like even though not as intricate as Veraggio. Plus I get more sparkle and coverage on her finger for a lower price. Anyway, the question I have is do you get many people that have a center princess and round sides like this would? I know look is subjective but do you think it is ok or would you suggest customizing it a little and switching the round for princess diamonds on the side? The other question relating to this is do you think that size princess stone would be too small as a center stone for this type of setting? I found a picture of probably about what it would look like but it is hard to without seeing it in person and I was wondering if you have seen anything like this? Here is the picture:
https://www.jamesallen.com/engagement-rings/vintage/18k-white-gold-royal-antique-style-round-shaped-diamond-engagement-ring-item-17720-purchased-4296?a_aid=dmnd1357

The only other thing is do you happen to know of any discount coupon codes that would apply to this setting/diamond combination? I’m sorry if I included anything that wasn’t necessary in those questions so that you had to read more or if you have answered anything like that previously and I missed it. Thank you so much for taking the time you do and I’m sure so many others like myself appreciate it greatly. Also, please let me know how I can make sure to help you when I purchase the ring.

Thank you. 

 I just wanted to thank you so much for all of your help. I ended up purchasing the ring from James Allen and I let the customer service rep know that I found out about James Allen from your site. Thank you.