Well the top item looks like a bone or ivory handled spoon of some sort....can't tell size but it might be for sugar . The hallmarks are not familiar, perhaps Dutch? Maybe Danish or Norwegean? Try a site called 925. The marks are not English, French, american nor Italian and I don't think they are Russian. I expect it's likely worth 60 to $100 Depending on if it's ivory or bone.
The plates are about 1900...nice but worth very little with the damage.

I'm wondering if the top item is some kind of serving tongs, with a hinge- thinking the round bit with an engraved daisy on it is where you press with your thumb.

Think you are right!...Sandwich tongs!

Ultimately the answer weather for sandwiches/petit fours or asparagus will depend on how they close. Usually those meant for sandwiches and cakes don't close entirely, while asparagus servers clamp down pretty well on the asparagus.
Now the question....who made them and from what country. I think we can pretty well date them at the 1860/1880 era from the britecut engravings....but maybe in Sweden or Norway, the dating of that style is different.
Where's Hester when we need her!?

Did you notice this item listed as sold in Olychic's second link? These are the silver marks on the OP's tongs. Barker brothers of Birmingham!

http://www.antiquesilverlondon.com/antique-silver-recently-sold/315-antique-victorian-silver-plated-asparagus-tongs.html

Not sure what you mean...The tongs marked sold are plate, the OPs' tongs are obviously silver and the marks are very different.
Unfortunately the OP's marks are so worn that I can't read them.....but looking again, that mark second from the bottom might be a leopard head without a crown....which makes it British and after 1822. So maybe the rest of the marks will be easier to find.

voila, good catch on the matching markings. I found this about Barker Brothers silver markings; this one seems to be an exact match, tho the poster's are a bit worn:

BARKER BROS
BARKER BROTHERS SILVERSMITHS LTD
BARKER ELLIS SILVER CO
Birmingham
Firm established in Birmingham in 1801 by Mary Barker. The business was
continued by her son William Barker in partnership with Creed under
the style Barker & Creed. In 1885 the firm traded under the style
Barker Brothers at Unity Works, Paradise Street, Birmingham as a
partnership of Herbert Edward Barker and Matthias Barker.
In 1903 they moved to new factory premises, Unity Works, Constitution Hill, Birmingham.
In
1907 the firm was converted into a limited liability company under the
style Barker Brothers Silversmiths Ltd and in the 1960s, merging with
Ellis & Co (Birmingham) Ltd, the firm changed to Barker Ellis Silver
Co Ltd.
On January 2, 1979, the firm obtained a Federal
registration in the USA for the trademarks Ellis & Co, Barker Ellis
and Ellis Barker (the marks were cancelled in 1988).
The company went into administration in 1992.
The firm used the trade marks BRITANOID, UNITY PLATE and THE HYGENIA

Here are a couple of links to more info from the above page:

http://www.silvercollection.it/electroplatesilverB.html

http://www.silvercollection.it/ENGLBARKERBROS.html

Looks like a match....but that would mean they are plate not sterling....
Good sleuthing!

No, Barker Brothers made sterling and also plate, which was marked EPNS. The marks on the OP's piece are their silver marks.

But they don't have the assay mark nor the town mark. British sterling always had the town mark, the lion or britannia signifying quality of silver content, date letter the mark of the maker and between 1784 or so until 1890 the monarch's head indicating that the duty had been paid. The only things I see on that are maker's mark....those are marks on plated silver....perhaps Sheffield plate which is different from Electroplate....but I don't see it mentioned that they did.

The B is for Barker brothers. The second B is for Birmingham. But the shield to the right has the EP for electroplate. It does not say sterling or 925.

The OP's piece is plated. But it is still a nice asparagus tong.

The backs of the plates are marked "wedgewood, england". One plate has a serious chip on its rim.