Given a travel related situation, and given a specific question about the situation, summarize the question into a title

[Q]: I'm from India and I applied for a Schengen visa to visit Sweden for a duration of 4 days and since I'm 18 years old, to prove my intent to return home after my visit, the Embassy wanted me to submit supporting documents such as the I-20 issued by my university in the USA. Since I didn't have the I-20 at the time and I didn't want to postpone my trip, I submitted a fake I-20. 

They granted me a visa but after a few days, called me back to tell me that my I-20 was deemed to have been forged and thus my visa had been annulled. The official reason on the rejection letter listed was "The information submitted regarding the justification for the purpose and conditions of the 
intended stay was not reliable". The consular official invited me to appeal the decision with genuine documents if I wished to but I've decided to simply cancel my trip for now.

I realize this was an insanely stupid thing to do and in hindsight, I wish I hadn't done it. I have since been issued a valid US F1 visa and also have my genuine I20. If I apply for a Schengen visa again, this time with genuine documents and the US visa stamped to my passport, will I get a visa or will my application be rejected right away?

[A]: Can I ever get a Schengen visa again?


[Q]: We are traveling to Istanbul, Turkey next month and we would like to take a day to visit Izmit.

With that plan in mind what we would like to do is travel from Istanbul (european side) to Izmit in the morning ~7am and return in the evening ~9pm.

Can you tell me how we can make this journey, preferably by train and where can we buy tickets from and what the approximate price is?

[A]: Train from Istanbul To Izmit and back


[Q]: Background

I've recently entered a relationship with a person from Canada. Part of that commitment involves visiting frequently throughout the year; this commonly involves me driving to pick her up, as opposed to flying to save cost, so she can stay with me in the US. She's planning on coming up to visit again for the entirety of the Summer (four to five months).

Extra information in case it has any impact:  


She is 20 years old.
She is a third-year university student and is committed to her program for another two years.
She has visited the US three times already this year. Twice to visit me (~five weeks in total); once to visit her friend (five days).
We've both lived in our respective countries all our lives.
I've only stayed in Canada with her for a few days at a time.

My Knowledge
Feel free to edit this information if any of it is misleading/incorrect.

The 180-day limitation mentioned in these threads [ 1 ][ 2 ] are for people who visit in one consecutive stay; not for totaling 180 days in the year.
She will be considered a resident alien of the US if she crosses the 183-day mathematical formula, as noted on this AmericanLaw website:


  A foreign national will meet the Substantial Presence Test if he or she is present in the United States for 31 days in the current year and the sum of the following:  
  
  
sum of the days present in the United States in the current year,  
one-third of the number of days present in the first preceding year,  
one sixth of the days present in the second preceding year equals or exceeds 183 days.

  
  If a Canadian meets the Substantial Presence Test but is ineligible to meet the Closer Connection Exception (i.e. since he or she is present in the United States for more than 183 days in the current year), he or she will be considered to be a resident alien of the United States. Resident aliens are taxed on worldwide income in the same manner as United States citizens.


Question

Are there any common limitations, mainly regarding stay durations or frequencies, that could make further visits throughout the year difficult or impossible?


Also, I fully understand that a visitation could be rejected for many reasons and that there's no guarantees regardless of how long of stay. I'm simply trying to avoid breaking any rules or missing any legal obligations that can come up from this international relationship. This is all foreign to me— pun was most certainly intended.

[A]:
What visitation limitations can come from a Canadian visiting the US for too long in the year?