What are algae?
Pond scums, terrestrial algae, snow algae, seaweeds, freshwater and marine phytoplankton etc. Plant body
relatively undifferentiated, no true roots, leaves, etc.
Algae are very simple chlorophyll-containing organisms: some say that they are plants; other say that the are not, calling them Protists. We use the term "algae" very loosely because defining them is very difficult. In general, we can say that they are simple organisms composed of one cell, or grouped together in colonies, or as organisms with many cells, sometimes collaborating together as simple tissues.
Most algae form some sort of spore, which is a
cell that is often motile and serves to reproduce the organism. Algae also have sex, often a very simple kind of sex where the algae themselves act as gametes, but sometimes very complicated with
egg and
sperm-like cells.
Some of the larger kelps have translocation but most do not. No need for water-conducting tissues as they are, at some stage, surrounded by water. Reproduce by spores of some kind. No seeds. Spores may be motile or non-motile; varies from phylum to phylum, e.g., the red and blue-green algae are non-flagellated.
Algae of one kind or another have been around for more than 2 billion years. We are still discovering new algae, sometimes whole groups of them at a time.
Algae of other groups usually have two flagella (singular: flagellum). Reproduction may be isogamous, anisogamous, or oogamous. Female gametangia are not enclosed by a wall of sterile cells as in higher cryptogams. Mostly autotrophic (photosynthetic), pigments very variable and are the basis of classification; all have chlorophyll a; some have b, others c; all have accessory pigments of some kind e.g. phycocyanin (bluish), phycoerythrin (reddish), carotenes (yellow-brown), xanthophylls (brown).
Some are heterotrophic (get energy from non-photosynthetic sources also). Great variation in size - unicellular and 3-10 µm (microns) to giant kelps up to 70 meters long and growing at up to 50 cm per day. Found in mostly aquatic situations (need water to reproduce and, generally, to photosynthesise).
Where are algae found? Algae are found just about everywhere on earth: in the sea, in our rivers and lakes, on soils and walls, in animals and plants (as symbionts - partners collaborating together); in fact just about everywhere where there is light with which to photosynthesise.
What are seaweeds?

Seaweeds are algae that liven in the sea or in brackish water. Scientists generally call them "benthic marine algae", which just means "attached algae that live in the sea". Seaweeds come in three basic colours: red, brown and green. Red and brown algae are almost exclusively marine, whilst green algae are also common in freshwater and in terrestrial situations.
Source: http://www.botany.uwc.ac.za
Algae is the plural; Alga is the singular. There is no such thing as "algaes".