Would it be possible for the Senate Democrats to block any of Donald Trump's nominations within the 52-48 Republican majority Senate? or would this be deemed implausible as a minority?
No, they cannot block the nominations.
Senate confirmations only require a simple majority vote as shown in this document from the State Department:
Under Senate Rule XXXI, the final question on a nomination is, “Will the Senate advise and consent to this nomination?” The Senate has three options: confirm, reject, or take no action on the nomination. Confirmation requires a simple majority vote.
However, they can stall the confirmations of his cabinet officials. The process is described in this article by CNN:
Once the committees have voted to send the nominations to the floor, Democrats, who have 48 seats compared to 52 for Republicans, can force delays for up to about one week per nominee, meaning it could take months to get through all the major posts.
But without GOP support, Democrats will be unable to use the ultimate stopping power of the filibuster to block nominees they oppose because in the last Congress they changed Senate rules -- over the objection of Republicans -- to lower the threshold of votes to overcome a filibuster of executive branch nominees from 60 to 51.
That means they best they can do is use procedural delays to stall a final confirmation vote.
They can insist on cloture votes for each nominee, and then use the entire amount of debate time allowed under the rules to delay speedy votes, and clog up floor time with lengthy floor speeches. This would mean each nominee could take up to a week to ultimately be confirmed and force McConnell to set aside other top legislative priorities -- like starting the process of repealing Obamacare.
That being said, it's very rare for nominees to be blocked. As seen in this article by FiveThirtyEight, only nine Cabinet appointees in history have been rejected.
The agencies will continue to function as per normal, but would have a lack of leadership if the appointments are blocked.
Can they block the nominations by themselves? No. In fact PBS reports:
Of those 25 [Democratic] senators [up for election in 2018], 13 are from states Trump captured or narrowly lost. Among those are Maine, Michigan, Pennsylvania and Wisconsin, which hadn’t backed a GOP presidential candidate since the 1980s
So building coalitions will be difficult if not impossible. Coalitions are likely to go the other way. So what can the Democratic Senators do?
They can play the race card, and have.
They can rely on a dishonest media to carry their argument for them.
But there is very little the Democratic Senators can do to stop his nominees.
Could Senate Democrats do anything to block Donald Trump's nominations?
Trump has the sole power in nominating those people.
but the democrats can certainly block the confirmation of those nominees, to the extent they can rally enough republicans to go with them.
it has been done by both parties.