I am in a very similar situation: new house, new crabapple tree ('snowdrift') at front, severe black/brown dots on the leaves. The snowdrift cultivar is supposed to have medium-high resistance to the scab... perhaps this fungus is a new strain? The tree was also planted 8" too deeply in our heavy clay, which suffocates the tree and makes it susceptible to disease. We just replanted this past weekend. From what I read, these fungus/bacterial infection does not live on the tree, they drop with the affected leaves and wait to re-infect the tree's new leaves next spring. Hope you are lucky to have powerful winds (we do) to minimize maintenance effort. All trees have their respective problems and benefits. Crabapples give stinky fruits and brown leaves in the fall in exchange for unequaled spring flowers, reduced insect problems and heavy clay tolerance. Even we originally wanted a serviceberry from the city (which gave it to our neighbor), we will take care of the crabapple as best as we can. In order to shift the attention in the fall, we planted a cutleaf staghorn sumac. Very, very nice shrub!

How about other trees in the same height category: paperbark maple Acer griseum corkscrew willow 'twisty baby' locust Redbud.....maybe a great native choice for you!!! or slower growing trees with outstanding foliage like some beech cultivars... 'roseomarginata' or some wonderful conifers that put on unbelievable spring shows like: Pinus contorta 'taylors sunburst' 3-4 WEEKS!!!of yellow new growth. See Photo. I could go on forever... red leaf japanese maple...bloodgood, atropurpureum, emperor(supposed to be the hardiest of all, emperor I or II) the debate with crabapples will always be...ARE THE WONDERFUL FLOWERS WORTH THE TROUBLE OF THE UNATTRACTIVE DISEASE RIDDEN FOLIAGE...AND IS ANYTHING WORTH SPRAYING IN MY GARDEN TO CONTROL DISEASE?...my honest opinion, there's plenty of wonderful plants that have outstanding characteristics that NEVER need to be sprayed. Blacklab Here is a link that might be useful:

The Norway rat is easily recognizable. That is the rat that is common in Nassau County. It is a big, Fat hefty rat and is much larger than most of the other rodents in the neighborhood. Norway rats can weigh 1¼ pounds. Roof rats stay at an agile ½ pound when fully grown. Roof rats have a longer tail, pointier snout and longer ears while the Norway ratÂs tail is shorter than the length of the body. Both rats have naked tails but the Norway ratÂs tail appears as two-tone from the partially haired skin. Rats have a high reproductive capacity and can compete well against other pests for our rubbish. Rats can reproduce all year long depending on environment and food. They usually reach their peak reproduction in the fall. Both species average about eight offspring per litter. A single female rat can produce as many as 80 rats in her lifetime. Gestation and weaning of young can last about two months; baby rats can be reproductively mature within three to four months. If you do the math, rat populations can build quite rapidly in good conditions.

I think you are worrying unnecessarily. Commercial orchardists routinely replace dead apple trees with a new one in the same spot. Very few diseases of any significance to apples will remain present in the soil and most of those can be circumvented by selecting a disease resistant cultivar (which Honeycrisp is) and by the appropriate rootstock. Your biggest worry is going to make sure you have the stump and roots of the old trees out of the way to make planting easy. btw, mummified fruit can just be as simple as fruit that never fell or eaten by any creatures and has started to deteriorate/decompose on the tree. And most old, untended apples will look 'diseased'......it is just a symptom of old age :-)