coordinate system - Measuring areas, lengths in specific regions (Australia, South East Asia)?

I'm in need to find a suitable projections to measure correctly areas and lengths for 2 areas of interest.

I want to measure both factors for:

1. First region Australia & New Zealand (1st region),


2. Second region - South East Asia defined as: Bornero, Honkong, Indonesia, Macao, Malyasia, Philipines, Singapoure, Thailand, Taiwan, Vietnam. (minlon: 94.89, minlat:-11.34, maxlong:141.056, maxlat:26.46)

In regards to Australia & New Zealand:

1. Equal area projection: I could find two suitable projection to measure areas in Australia GDA94 / Australian Albers (EPSG:3577) and the Australian Albers (EPSG:17365).

What about having a proper projection to measure areas at once in Australia and New Zeland?

Is there any ready to use projection to do it or should I customize one of currently available, if so the question is how?

How does such projection measure area of relatively small shapes like shapes of the buildings in country?

Does the area of interest the projection is applicable for somehow correspond to the size/ area of the object I would like to measure?

2. Equidistance projection

Does the term distance correspond to the length in my understanding?

For example I want to measure the length of each road I do have in the Australia's dataset I work with, but reading the definitions of equidistance projections I'm a litlle bit confused while in fact they're saying:

Equidistant conic projection - It has the useful property that distances along the meridians are proportionately correct, Equidistant conic projection - It has the useful properties that all points on the map are at proportionately correct distances from the center point.

What about measuring the length?

Does the equidistance projection work for that, if not what would be the best option to go for region1/ region2 from my definition?