My grandfather used to do this all the time And it's really easy:

Start with a fresh avocado pip, straight out the flesh of a ripe fruit.
then get a smallish jar, just big enough for the avocado pip to fit and stick 4 toothpicks in the avo around the edge to be able to hold it sitting in a jar with with pointy side down. Fill the jar enough that the bottom of the pip is always in water. Wait till it sprouts

My mangos do seem to live for a while, then fade. I have had these two for eighteen months, a new record. There isn't really much long term hope for them as I have my doubts they can forever live in a pot.
All my fruit trees outside are grafted to ensure good fruit so I am going to take the same approach with the citrus.
The allspice should recover. I have done this too. Give it a good dose of an organic fertilizer (won't hurt roots but delivers plenty of nutrients for good growth) and that will help.
The systemics that work with mites are created for roses and will say that they get rid of mites. Hybrid tea roses are often delicate and tend to die rather easily so the products made for them are very effective. As pointed out, a systemic should never be used with a plant that produces edible fruit or leaves.
I have never tried to grow an avacado but my book (The Houseplant Expert, Dr. D.G. Hessayon) says to push the blunt end into the soil and leave the pointed end exposed, keep warm until leaves appear (this is pretty much copied from the book). I hope this helps.

thank you both for your help, if this works will try mango seeds next!

I’ve got

Bell peppers (red, yellow and green)
Aloe Vera
Hibiscus pink and blue
Mexican sunflower
Shrub rose
Lily of Nile

The easier question for me to answer is what do I NOT grow, lol... Here's a fraction of the basement during winter showing a bit of my makeshift winter greenhouse.
http://img.tapatalk.com/d/12/10/31/ymy5a8yd.jpg
Of course, this doesn't include those plants scattered around the house and those grown outside year around in our heavily planted yard, lol...

BTW, I think we have the freshest house air on Te block during the winter, lol...

WOW !!!!!!!!!

LOL... People are Usually shocked when they see our backyard for the first time from Spring to fall. There are all sorts of tropical plants that are large that you would never find in St. Louis otherwise, Including a 12 foot rubber plant. It's like a tropical oasis in the middle of the U.S!

I love it! I use the 'air purifying' argument to justify why I have so many plants. Your orchids must benefit from all the humidity--I know mine do. I see the hibiscus, mine are now regulated to a north window so they will stop blooming until I put them outside in the spring. I think collecting plants is a great hobby! :)

Wow Paul. And I thought I had it bad. For me the short answer is anything with roots, shoots, or leaves.

As a horticulturist who lives near one botanic garden and works near another I have collected some unusual stuff over the years. And my wife complains I have too many. After seeing the picture of your basement, all I can say is "I bow before the master!" :bowing

Cheers.
Jim