Which features make a language easier to learn for children learning a constructed language as L1? Are children learning a language with these features able to learn the language faster than a natural, irregular language without some of these features?
Difficult question. I think regularity would speed up learning, as children during language learning overgeneralise (see experiments with English past tense endings). Thus instead of learning the correct exceptions at a later stage the corresponding feature would have been learned earlier.
There is a programme for teaching Esperanto as a first foreign language, as it can be used to increase second language awareness and is supposed to make learning a natural foreign language easier. You don't have to worry about exceptions, for one thing, so you can teach the concept without having to hedge your explanations by listing all the cases where it's different.
My personal view on 'difficulty' of different languages is that all languages are about equally difficult. Some languages are easier/simpler regarding some features (English inflectional morphology), but make up for that in others (vast number of near-synonyms with different distributional characteristics in English). Toki Pona is a very simple language (120 words, virtually no syntactic complexity), so you can learn it almost in a day, but it is very hard to express complicated narratives, and an equivalent text in a more complex language would be far more concise.
Learning Esperanto is reasonably easy, but then you look at how people actually use it in everyday interactions, and you find that it is more difficult than you imagined: there are a lot of the smaller particles that make it tricky to understand for a beginner. But the 'early' sentences composed when the language was still fairly new are a lot simpler. However, they were not suitable for encoding all the pragmatic and other information people need for an everyday language.
So, there are undoubtedly features that make it easier for children to learn a language as L1, but the question is "what for?" It's a bit like learning Lisp programming: understanding the syntax takes literally ten minutes, but that does not mean you can write useful programs in it after that. Languages are more than the sum of syntax and vocabulary, and if there was a language that was easier to learn and use than other languages, and had equal expressive power, then we would all be speaking it already.
Children learning an L1 have most of the same challenges as people in general learning an L2. Children learning a conlang, will have all of the problems of children learning a non-community language from a parent-- mostly problems of exposure. Kids need to hear the language for something like 20+ hours a week, less than that and they start to learn a pidgin form that is simplified. See the literature on language death for more about that process.
A rich vocabulary is hard. Teachers of languages say that the shear amount of vocabulary you need to learn is a major barrier to learning a language. This is why auxlangs try to pick words that are highly similar to what someone already knows. toki pona takes the idea of vocabulary reduction to about as far as it can go, but in my experience with it, it still feels like you need to memorize about 3000 set phrases whose meaning can't easily be guessed from the parts.
Morphology is hard. Analytic languages are going to be less difficult. In communities where a polysynthetic language is dying, the kids start using it as if it were analytic, i.e. with sentences with more words instead of one spectacularly complex verb.
Lexicalized grammar is hard. This is when you make up words instead of applying a grammatical rule. For example, in German, you have to just memorize most plurals as a second word. It is easy to accidentally create lexicalizations if you mother tongue has them. For example, in some language antonyms are phrasal or morphological modifications of a base word, in English and other languages, antonyms often are a separate word. My son right now is at the point where he over-regularized past tense English verbs, an indication that lexical past tense forms, (see, saw, eat, ate, etc) are hard, even for kids.
Human beings first develop with a sense of Self and not being able to distinguish between "Self" and "The World". Things are seen as "Images" and "Objects", only later are abstract ideas understood. Human languages started off as SOV (Subject-Object-Verb) but later changed to different word orders.
With that being said, these features would make it easier to learn languages.
Common Phonemes (/m/, /k/, /i/, /a/, /j/, /p/, /u/, /w/)
No Consonant Clusters ( mk, mp, kp, pk)
Noun based (let verbs and adjectives derived from nouns)
Let any complex words have it's root from the simple (For Example: "Hospital" could be "Health-House" or "Healing Place").
Just like human beings start of learning simple things, then complex, let all "big" words be form from compounds of smaller ones.
- Remember language Universals. Frontal vowels (/i/) are usually used in words that represent smallness, sharpness, brightness, closeness, and hapiness. The sound /i/ uses the same muscles as when a human being smiles.
Back vowels (/u/) are usually used in words that represent bigness, depth, roundness, smoothness, darkness, dirtiness, far-distance, and gloominess.
Toki Pona has some of the features of what an easy language would look like. Good luck to inventing an easy/minimalist language. Cheers!