Angie_H,
Yours are interesting questions, which even contemporaries of the Imperial Family posed themselves. From what I have read, it seems that Alexandra's main motivation in isolating her children from the outside world was to protect them from what she perceived as the many negative influences surrounding them. It seems that many of their contemporaries probably lacked the solid moral values that Alexandra tried to instill in her children, as they were more interested in partying and decadence than in a quiet home life centered around family. In this, I find the Imperial Family to have been more like ordinary people than royalty, as their core traditional values dictated family first as opposed to lavish parties and self-indulgence. As a concerned mother, Alexandra tried to shelter her children from that type of world. Indeed, I think that is what many mothers even today wish they could do, to protect their children from negative outside influences and keep only the good around them. However, as ordinary folks we are unable to do so, as our lives in this day and age have children necessarily exposed to their peers in school and later when they enter the workforce. It is just a normal part of life for us. Our children cannot be secluded in a palace surrounded only by their close family and carefully selected people.
Alexandra also thought that the children could keep themselves occupied amongst each other, without the need to bring in outsiders. As there were four sisters with much in common, they were each other's best playmates. Of course, it could grow boring dealing with the same people day in and day out, and this was seen by outsiders to be detrimental to the children's normal social development, so they tried to help expand their horizons. For instance, their aunt, the Grand Duchess Olga, gave small weekend parties to which the Grand Duchesses eagerly attended and apparently delighted in. Of course, the young people at those parties were very carefully selected to ensure Alexandra's high standards, but they were a diversion nonetheless. Alexei also had outside children brought in to play with him; again, carefully selected sons of officers, but other children nevertheless. The G.D. Tatiana in particular seemed to eagerly seek the companionship of others, as she was naturally outgoing and friendly and wanted friends outside of her tight family circle, but this was not possible.
Alexandra did in fact also consider her daughters as companions, as it has been stated in various books that whenever the girls went out on walking excursions and rides, one of them always stayed behind with their mother, who rarely ventured outside on such journeys. The girls apparently did not mind doing this, and each took turns performing this task. I don't know if this attitude of Alexandra's was due to Queen Victoria's influence, or just due to the fact that she couldn't join their excursions due to health reasons and didn't want to be left alone. The girls apparently considered it as their duty and did not mind keeping their mother company.
The Grand Duchesses were also indeed said to be quite naive about the outside world. For instance, they did not know much about the value of money and buying items in stores, which they were only able to do while on holidays abroad, and contemporaries noted that they seemed immature for their age, in the way that they expressed themselves and acted. Their mother certainly and unapologetically wanted to keep them as children for as long as possible. I don't know if she would have insisted all of her daughters to stay in Russia after their marriages, as I think it was probably inevitable that at least one of them would have been married to a foreigner and gone to live abroad. For instance, I have read that had the revolution not occurred, the G.D. Maria may very well have been married to her cousin Prince Louis Mountbatten of England, who was madly in love with her and whom apparently she had a liking to as well. As far as Olga goes, as you correctly stated, she made the decision herself not to leave Russia and didn't seem to be influenced by her mother in that decision, as she was very steadfast about it and seemed to come to it on her own.
As far as your last question, it is sometimes hard to believe in these cynical times that these girls were as constantly loving and devoted to each other as they were made out to be, but apparently that is really how they were, as evident in their diaries, letters, and contemporary accounts. I am sure they did get on each other's nerves from time to time. There are in fact examples of this in their letters (from memory, i.e., Olga trying to slap Anastasia's hand away from her nose as she was picking it, etc.), but they seemed to be fleeting moments. From all accounts, the girls realized that they lived in a "gilded cage," but didn't seem to mind it - instead, they seemed to treasure it and couldn't imagine any other way of life. Indeed, one must admit that despite their isolation their lives were idyllic until the last few years.