Are EU border guards there right now? Are they supposed to do the job or somebody else?
No, whatever inspections may be necessary should be carried out by British personnel, e.g. at the Points of Entry operated by Northern Ireland's Department of Agriculture, Environment and Rural Affairs. Similarly, declarations to determine whether goods are “at risk” of entering the EU and VAT payments will need to be made through Her Majesty's Revenue and Customs.
Generally speaking, customs inspections in the EU are carried out by the relevant national agencies or departments, who are in charge of applying EU law and collecting duties on behalf of the EU (and VAT, which is shared between member states and the EU) so there isn't any established EU border force that would be ready to pick up the task. Frontex recently started setting up an independent uniformed “European Border and Coast Guard Agency” but it's intended to deal with police/immigration matters rather than customs issues and can only assist member states in very specific cases.
There is a specialised committee “on implementation of the Protocol on Ireland/Northern Ireland” and reviews planned in the original agreement to ensure this setup is working and the UK is not simply ignoring the rules but the general assumption is that it can be trusted to carry out the necessary checks on the ground. In any case, the presence of foreign uniformed law enforcement officers is unlikely to be acceptable to the UK.
How does the deal impact the matter? EU border guards still need to make sure that the goods are indeed British, especially after the UK strikes its first FTA with a third country. The checks add up to the cost of exports, don't they? Has it been estimated yet?
It has been clear for a long time that the deal would not be enough to make checks completely unnecessary. My understanding is that it helps a bit as most goods imported into Northern Ireland from Great Britain will be deemed “not at risk” by virtue of the zero tariff.
The backstop and then the Nothern Ireland protocol were always designed (with some contructive ambiguity) to minimise checks between Northern Ireland and Great Britain (while eliminating them completely at the Nothern Ireland/Republic of Ireland border). So with respect to Northern Ireland the main issue is not checks and delays but a new de facto regulatory border and additional paperwork.
It doesn't completely eliminate physical checks (especially but not only for live animals, plants and agri-food goods) but most of these formalities can be done electronically. Some certification is also performed by third parties (e.g. Official Veterinarians) and all this does indeed have a cost. I assume costs estimates exist, possibly not all of them public, but I don't know much about them.
Regular British citizens are also now searched and stuff like at a regular international border, aren't they?
No, that's not the case and is not particularly likely to be an issue. Importantly, even at regular EU external borders, customs inspections are relatively rare. Systematic checks are reserved for immigration matters (Schengen external border) and both the UK and Ireland are outside of the Schengen area and have their own arrangements in this domain.
At an international airport in the Schengen area, you can witness how this works for private citizens yourself. If you come from outside the Schengen area, you are supposed to undergo an entry immigration check where everybody has to queue up and show their passport (possibly through an automated gate) before going to the luggage collection area. After that, most passengers just walk out through the green lane, customs agents are often present (sometimes stopping people at random, sometimes just watching) or watching remotely but not everybody is asked to empty their bags or even merely answer questions, far from it.
At a regular international border (say between Greece and North Macedonia), I think each and every lorry needs to wait and be inspected in some way, cars have to stop, people have to show their passport but even there private citizens are not “searched”.
At the Swiss border (outside of the customs union but closely associated with the EU and inside the Schengen area so that immigration checks are not necessary), infrastructure still exists, border guards are present and may stop people but most just drive/walk through without interacting with anyone. For traded goods, most of the formalities are dealt with electronically and only some lorries need to be physically inspected.
The Swiss solution is not readily applicable here and it remains to be seen how well all this works in the long run but imports by private citizens do not seem to be very high up the list of concerns.
The Johnson government showed reluctance to actually accept the EU-enforced Irish border even though they had agreed on that (they hoped to push through a piece of legislature allowing them to neglect that part of the deal last year, you may remember). Are there any rumors or anything on whether they have any other plans to derail that arrangement? It clashes with Johnson's whole "sovereignty" narrative, he must be unhappy.
Much has been written on the goal of this manoeuver. I am not sure Johnson personnally cares that much about it. At the moment the British government seems keener on highlighting its ability to actually get Brexit done rather than complaining about the details.