An example explanation ...
I believe they:
the fund has "one big bank account" with all the/any cash and obviously "one big holding" of the various stocks
they calculate/decide on the current annual expenses. for example 5 staff members, 13 desk rentals, electricity bill, total is $2.5m
They divide $2.5m by 365
Each day they literally take that much out of the big bank account. (selling stocks if necessary, blah blah)
Note that on your account "when you log in" they never "deduct anything from your account".
You account basically shows their current "grand total" divided by your share.
They already take the "costs for desks etc" out of the grand total, indeed on a daily basis.
Your specific examples,
Is every purchase of the fund reduced by 0.055%?
No. Simply, expenses are deducted every day (adding to the overall annual expense target).
So, say in theory a million people paid in $1000 each to the fund so they have $1b sitting there. So far they have not bought one stock. Each day an amount (call it $5000) is deducted from the cash pile and goes to the "expenses" pile.
Say 100 days have gone by and still no stock purchase. So, the cash pile is down $500,000.
They suddenly decide to buy every penny of Apple stock. So yes, instead of $10b they would only be buying $9.995b of Apple.
So this - "Is every purchase of the fund reduced by 0.055%?" - is not really correct, it's more along the lines of "they have slightly less available to buy stock than the overall sum of contributions"
So if a fund has a cost of $100/share
it does not work like that, no
and $1000 is contributed, its $55 taken by the manager and then 9.45 shares are purchased?
No. The $1000 just goes in the kitty. The overall kitty is decreased every single day by the expenses removal that day (which is indeed roughly fixed, perhaps "2 million a year", it's not a percentage as such). (Indeed also don't forget that as more people put in money, the percentage spent on expenses decreases.)