No, what goes in does not automatically come out! Otherwise babies on formula would be eating grass and cow cake
What you eat goes into your stomach and undergoes the usual digestive goings-on. Some elements of these foods will pass through to the blood and thence to the milk, in very tiny amounts. Flavours for instance, have been shown to get through (this is a good thing - prepares the baby for the usual diet in that society). 'Foreign' proteins can get through - hence the nuts thing and the dairy thing, but these would not be at all harmful in healthy non-allergic babies, and again, would be a good, preparing thing.
I have no idea about strawberries, sorry - I suspect anecdotal evidence only but that's not to say it ain't true. There is something in a strawberry that is allergenic, I know - maybe it gets into the milk.
Other elements of food don't get anywhere near the milk. So eating Bran Flakes will not help your baby's constipation, because the fibre part of the food stays in your gut and affects your gut only. That's just an example. The majority of mothers can eat their usual foods without any concern at all.
Expressed breast milk that is notably creamy - see your post ohforfoxsake - does not reflect diet in any way.
The type of fats in milk can be affected by diet, marginally, but not the quantity, which is affected by the amount of milk in the breast at the time.
Breasts which have less milk in at that particular moment will have creamier milk - this is normal, and the fat content of a mother's milk varies a lot. It doesn't matter. The baby sorts it out!
You may have expressed more thoroughly with baby no. 1, maybe, or had a different pump, or a different technique or just expressed at different times.
Health care professionals go on about diet and breastfeeding and what you should eat to make milk 'better' - when they do this, it is a sure sign they know very little about bf!