Apparently, Eagle doesn't allow vias in footprints (only pads). Markers will work to check alignment, but for creating them you can write a script that takes the part designator as parameter, and uses it to extract location and rotation to place the vias at the correct coordinates. Something like place_bpf_vias(part_designator)
Because the vias are not linked to the part, you will have an issue when moving it, so first select it with the vias as a group.
Rarely will you need or want to put the capacitor exactly on the power pad. Yes, you'll want to keep it close for best decoupling, but just outside the IC courtyard is very good.
As Andy already mentioned, it's generally not recommended to use plated through holes for BGA pads. Even with microvias, there is a tendency for solder to want to wick through the hole and you may end up with voids where your solder balls formerly were.
As you mentioned, filling and capping the via will prevent this, but at added cost.
Most people use dogbones to route out from the BGA pad to avoid putting a via in the pad:
You can make one of these for each pad you need to get to a different layer - typically all PWR and GND pads will connect to their respective planes with one of these vias.
Depending on how big your BGA package is, you may be able to route the rest of the signals directly out on the component layer, avoiding a via entirely.
Speaking of planes, you don't mention how many layers you are planning to use for this PCB. I would say 4 is a minimum for most BGA layouts. If you have a PWR and GND plane you can then use a dogbone and drop a via to connect to the respective plane. Then you can place your capacitor somewhere more comfortable and connect it to the planes with vias.
Eventually you'll need enough layers to bring each signal out without hitting a nearby via (through hole) or trace. Blind vias (vias that go from an outside layer to an inner one without going all the way through) help immensely but again, add cost.
This image from Altium shows a 4-layer fanout for a small BGA:
You can see that you start to have difficulty routing out the further in you go. That page from Altium has some good tips and shows how to use their tools to help.
Mentor Graphics just published a book by Charles Pfeil covering more than you will ever care to know about BGA routing. You can find it here (free download, but requires registration):
https://www.mentor.com/pcb/resources/overview/bga-breakouts-and-routing-5e5d097e-55e4-47f6-b5af-dcc55e1892b0
Altium fanout page:
http://techdocs.altium.com/display/ADOH/Fanout+and+Escape+Routes
Best Answer
As @JRE pointed out, these red circles are a keepout area for signals not belonging to the pad's net.
You will need to use a footprint where the pads have less "security margin" around the pads. You can adjust that under Tools->Design Rules by reducing the "Clearance".
Which brings me to the question: What kind of footprint is that? It doesn't have a component outline...