Welcome to Tnet and my sympathies for the passing of your grandmother.
That’s a nice collection and I’m sure she had fun putting it together but, as said, these pieces have no great value. Enjoy them in the same way that I'm sure your grandmother did. Technically, there’s nothing there which is antique (taking the convention that an antique is more than 100 years old). They’re mid-20th Century as copies of, or borrowing from, earlier styles.
The blue-on-white demi-tasse and saucer is from the time when Avon expanded its line of novelty containers for perfumes and colognes to include collectibles such as decorative china, beer-steins, bells, figurines, Christmas ornaments and such during the 1970s and 1980s. I’ve seen that same design with Avon’s mark and a fuller description on the bottom that says “Medici Porcelain, Florence c.1560” (which is what it’s styled on) and a copyright date of 1984.
The pieces with the foil labels saying “Royal Sealy, Japan” are likely from the 1950s or possibly as late as the 1970s. Royal Sealy was the trade name used by an importer of Japanese porcelain in operation from the early 1940s (and then again after the War) producing in imitation of earlier European styles. Obviously there were no imports following Pearl Harbour and, when production resumed after the war, the required wording for origin marking was “Occupied Japan” until 1952 and then “Japan” thereafter. In that post-war period, foil labels carrying the origin and other marks became a preferred alternative to printed marks on the pieces. The labels could be removed, along with any stigma associated with lingering ill-feeling about buying Japanese goods.
The ”Kent” bone china is from Taylor & Kent of Longton, Stoke-on-Trent in England. Although they were founded in 1876 (many sources perpetuate an incorrect date of 1867 arising from a misprint somewhere), your particular mark was in use between c.1951-1961 after which they used the trade name “Elizabethan China”.
The “Crowned M” I can’t attribute, but the comments above about “Japan” marks and likely post-1952 dating also apply here. It might be for what became the “Noritake” company, originally established by the Morimura Brothers in New York in 1876 as an importer of Japanese porcelain from their own factories. They used several hundred different marks, many of which have a stylised letter ‘M’ for ‘Morimura’, with and without a crown above. Noritake stopped importing to the US in 1940 and resumed several years after the war ended.
It's not clear if the ‘Crowned M’ mark you’re showing in picture #11 relates to the rose-decorated cup & saucer in picture #13, but I’m guessing it does. I’ve seen exactly that pattern, known as “Moss Rose” and branded “Bond Ware” on porcelain sold by Lipper & Mann, although the pieces are marked as such on the bottom. L&M were founded in 1946 in New York as an importer of fine glass and ceramics from Czechoslovakia and other European countries but three years later expanded to include porcelain imports from Japan. Some American companies preferred to have their own exclusive mark on imported pieces rather than the actual manufacturer’s mark (although the ‘Japan’ indication couldn’t be avoided) and my guess would be that yours and the L&M pieces came from the same factory… perhaps Noritake.
The “Hour of Power” mark in picture #13, I assume relates to the cup & saucer, sugar bowl and milk jug in pictures #10 and #12. Doubtless you’ve Googled that mark, found the rose pattern, and know that it relates to fund-raiser ‘souvenirs’ marketed by the Christian evangelist Robert Harold Schuller, founder of the ‘Crystal Cathedral’ in Garden Grove, California. He hosted a weekly “Hour of Power” TV program from 1970 until his retirement in 2010.
Sadly, none of these pieces would likely sell for anything beyond $10-15 or so, and without any particular value benefit where you have a set. The Avon piece might fetch a little more since Avon is generally a quite collectible name.
Hope that helps.