Are you building more than one of each service? When starting out you don't have that luxury. You have to accept you can't get perfect coverage. Don't worry about fire stations letting things burn down (as an example). The coverage is just its specialty effect (lower chance of fire starting for this example) and its effect on property values. They will send fire trucks anywhere that has road access. Same for the rest.
Eventually you'll be able to get full coverage of everything. Once you have all/most services unlocked you can get buildings to upgrade (by providing services) which pay more taxes.
Agree.
From the very beginning reduce your power and water budget to 50% (lowest amount possible). Then keep it at a point that is slightly/moderately more than what your city requires, at any given time. Monitor your water and power because you will need to constantly increase it to keep up with demand as your city grows. Increasing power and water in 3-to-5% increments is good/acceptable (this way, you aren't going to the budget every 5 minutes or so).
Then when you decide to finally add fire/police/medical,
always build only one structure, and start it off at 50% budget (again, lowest possible). When you notice a lot of those notification/trouble icons on your map, of one particular type, then slightly increase the budget for that particular service (maybe in 10% increments). Don't panic if you just see one, two or three of these icons, that is normal. Only "react" to correct the issue if you notice a handful of the same icon (but also consider the advise in the next paragraph).
Also take notice that these notification/trouble icons have two stages of severity. If you click on a building with an icon, you get an info window for that structure, and you will see the trouble icon defined (spelled-out) for you in words.
The background color behind this wording will first be a brownish color, which means it is only a level one issue (don't panic at this level). After an additional amount of time, if the issue is not resolved, this background color will change to a brick-red color which is a level two issue (now monitor and execute a plan of attack). If the problem is still not resolved after some time as a level two issue, then your structure is penalized (usually it is abandoned or it burns down) or there is some other consequence towards your city. Note that the background color directly in the icon itself, will tell you if it is a level one or two issue (not all the icons, but I think most of them do this).
And as Fox above has indicated, it is usually never a good idea to have your budget above 100% for that particular service, unless you do it for a quick short-term solution (an emergency). So, once you reach 100% and you need more of that particular service, then add/buy another structure (one only). After placing this new structure you can then usually lower the budget for that service slightly (to 70-to-85% or so). Then after growing your city more and more, you will eventually reach 100% once again ("rinse and repeat" the process).